[Scipy-svn] r4197 - trunk/scipy/special/specfun
scipy-svn at scipy.org
scipy-svn at scipy.org
Tue Apr 29 14:27:04 EDT 2008
Author: cookedm
Date: 2008-04-29 13:27:02 -0500 (Tue, 29 Apr 2008)
New Revision: 4197
Modified:
trunk/scipy/special/specfun/specfun.f
Log:
scipy/special/specfun/specfun.f: Convert to UTF-8
I don't know what the previous encoding was. This just affects the comments.
Modified: trunk/scipy/special/specfun/specfun.f
===================================================================
--- trunk/scipy/special/specfun/specfun.f 2008-04-28 20:23:26 UTC (rev 4196)
+++ trunk/scipy/special/specfun/specfun.f 2008-04-29 18:27:02 UTC (rev 4197)
@@ -21,7 +21,7 @@
C Input: z --- complex argument of D(z)
C n --- Order of D(z) (n = 0,-1,-2,...)
C Output: CDN --- Dn(z)
-C Routine called: GAIH for computing â(x), x=n/2 (n=1,2,...)
+C Routine called: GAIH for computing Г(x), x=n/2 (n=1,2,...)
C ===========================================================
C
IMPLICIT DOUBLE PRECISION (A-B,D-H,O-Y)
@@ -136,8 +136,8 @@
C Purpose: Compute the associated Legendre functions of the
C second kind, Qmn(x) and Qmn'(x)
C Input : x --- Argument of Qmn(x)
-C m --- Order of Qmn(x) ( m = 0,1,2,úúú )
-C n --- Degree of Qmn(x) ( n = 0,1,2,úúú )
+C m --- Order of Qmn(x) ( m = 0,1,2,… )
+C n --- Degree of Qmn(x) ( n = 0,1,2,… )
C mm --- Physical dimension of QM and QD
C Output: QM(m,n) --- Qmn(x)
C QD(m,n) --- Qmn'(x)
@@ -294,7 +294,7 @@
C Input: x --- Argument
C va --- Order
C Output: PV --- Vv(x)
-C Routine called : GAMMA2 for computing â(x)
+C Routine called : GAMMA2 for computing Г(x)
C ===================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -345,7 +345,7 @@
C Purpose: Compute the zeros of Bessel functions Jn(x) and
C Jn'(x), and arrange them in the order of their
C magnitudes
-C Input : NT --- Number of total zeros ( NT ó 1200 )
+C Input : NT --- Number of total zeros ( NT ≤ 1200 )
C Output: ZO(L) --- Value of the L-th zero of Jn(x)
C and Jn'(x)
C N(L) --- n, order of Jn(x) or Jn'(x) associated
@@ -866,16 +866,16 @@
C
C =====================================================
C Purpose: Compute the initial characteristic value of
-C Mathieu functions for m ó 12 or q ó 300 or
-C q ò m*m
+C Mathieu functions for m ≤ 12 or q ≤ 300 or
+C q ≥ m*m
C Input : m --- Order of Mathieu functions
C q --- Parameter of Mathieu functions
C Output: A0 --- Characteristic value
C Routines called:
C (1) CVQM for computing initial characteristic
-C value for q ó 3*m
+C value for q ≤ 3*m
C (2) CVQL for computing initial characteristic
-C value for q ò m*m
+C value for q ≥ m*m
C ====================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1033,7 +1033,7 @@
C
C =====================================================
C Purpose: Compute the characteristic value of Mathieu
-C functions for q ó m*m
+C functions for q ≤ m*m
C Input : m --- Order of Mathieu functions
C q --- Parameter of Mathieu functions
C Output: A0 --- Initial characteristic value
@@ -1054,7 +1054,7 @@
C
C ========================================================
C Purpose: Compute the characteristic value of Mathieu
-C functions for q ò 3m
+C functions for q ≥ 3m
C Input : m --- Order of Mathieu functions
C q --- Parameter of Mathieu functions
C Output: A0 --- Initial characteristic value
@@ -1246,10 +1246,10 @@
C
C ==========================================================
C Purpose: Integrate [1-J0(t)]/t with respect to t from 0
-C to x, and Y0(t)/t with respect to t from x to ì
-C Input : x --- Variable in the limits ( x ò 0 )
+C to x, and Y0(t)/t with respect to t from x to ∞
+C Input : x --- Variable in the limits ( x ≥ 0 )
C Output: TTJ --- Integration of [1-J0(t)]/t from 0 to x
-C TTY --- Integration of Y0(t)/t from x to ì
+C TTY --- Integration of Y0(t)/t from x to ∞
C ==========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1302,10 +1302,10 @@
C
C =========================================================
C Purpose: Integrate [1-J0(t)]/t with respect to t from 0
-C to x, and Y0(t)/t with respect to t from x to ì
-C Input : x --- Variable in the limits ( x ò 0 )
+C to x, and Y0(t)/t with respect to t from x to ∞
+C Input : x --- Variable in the limits ( x ≥ 0 )
C Output: TTJ --- Integration of [1-J0(t)]/t from 0 to x
-C TTY --- Integration of Y0(t)/t from x to ì
+C TTY --- Integration of Y0(t)/t from x to ∞
C =========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1601,9 +1601,9 @@
C (2) CV0 for finding initial characteristic
C values using polynomial approximation
C (3) CVQM for computing initial characteristic
-C values for q ó 3*m
+C values for q ≤ 3*m
C (3) CVQL for computing initial characteristic
-C values for q ò m*m
+C values for q ≥ m*m
C ======================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1917,9 +1917,9 @@
SUBROUTINE GAM0 (X,GA)
C
C ================================================
-C Purpose: Compute gamma function â(x)
-C Input : x --- Argument of â(x) ( |x| ó 1 )
-C Output: GA --- â(x)
+C Purpose: Compute gamma function Г(x)
+C Input : x --- Argument of Г(x) ( |x| ≤ 1 )
+C Output: GA --- Г(x)
C ================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -1950,7 +1950,7 @@
C
C =============================================
C Purpose: Compute cosine and sine integrals
-C Si(x) and Ci(x) ( x ò 0 )
+C Si(x) and Ci(x) ( x ≥ 0 )
C Input : x --- Argument of Ci(x) and Si(x)
C Output: CI --- Ci(x)
C SI --- Si(x)
@@ -2050,7 +2050,7 @@
C
C =============================================
C Purpose: Compute cosine and sine integrals
-C Si(x) and Ci(x) ( x ò 0 )
+C Si(x) and Ci(x) ( x ≥ 0 )
C Input : x --- Argument of Ci(x) and Si(x)
C Output: CI --- Ci(x)
C SI --- Si(x)
@@ -2134,7 +2134,7 @@
C ===========================================================
C Purpose: Evaluate the integral of modified Struve function
C L0(t) with respect to t from 0 to x
-C Input : x --- Upper limit ( x ò 0 )
+C Input : x --- Upper limit ( x ≥ 0 )
C Output: TL0 --- Integration of L0(t) from 0 to x
C ===========================================================
C
@@ -2186,7 +2186,7 @@
C
C ================================================
C Purpose: Compute modified Struve function L1(x)
-C Input : x --- Argument of L1(x) ( x ò 0 )
+C Input : x --- Argument of L1(x) ( x ≥ 0 )
C Output: SL1 --- L1(x)
C ================================================
C
@@ -2291,7 +2291,7 @@
C
C ================================================
C Purpose: Compute modified Struve function L0(x)
-C Input : x --- Argument of L0(x) ( x ò 0 )
+C Input : x --- Argument of L0(x) ( x ≥ 0 )
C Output: SL0 --- L0(x)
C ================================================
C
@@ -2551,10 +2551,10 @@
C Input : M --- Maximum order of Mathieu functions
C q --- Parameter of Mathieu functions
C KD --- Case code
-C KD=1 for cem(x,q) ( m = 0,2,4,úúú )
-C KD=2 for cem(x,q) ( m = 1,3,5,úúú )
-C KD=3 for sem(x,q) ( m = 1,3,5,úúú )
-C KD=4 for sem(x,q) ( m = 2,4,6,úúú )
+C KD=1 for cem(x,q) ( m = 0,2,4,… )
+C KD=2 for cem(x,q) ( m = 1,3,5,… )
+C KD=3 for sem(x,q) ( m = 1,3,5,… )
+C KD=4 for sem(x,q) ( m = 2,4,6,… )
C Output: CV(I) --- Characteristic values; I = 1,2,3,...
C For KD=1, CV(1), CV(2), CV(3),..., correspond to
C the characteristic values of cem for m = 0,2,4,...
@@ -2663,10 +2663,10 @@
C
C =========================================================
C Purpose: Integrate [I0(t)-1]/t with respect to t from 0
-C to x, and K0(t)/t with respect to t from x to ì
-C Input : x --- Variable in the limits ( x ò 0 )
+C to x, and K0(t)/t with respect to t from x to ∞
+C Input : x --- Variable in the limits ( x ≥ 0 )
C Output: TTI --- Integration of [I0(t)-1]/t from 0 to x
-C TTK --- Integration of K0(t)/t from x to ì
+C TTK --- Integration of K0(t)/t from x to ∞
C =========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -2719,7 +2719,7 @@
C ====================================================
C Purpose: Compute Legendre functions Qn(x) & Qn'(x)
C Input : x --- Argument of Qn(x)
-C n --- Degree of Qn(x) ( n = 0,1,2,úúú)
+C n --- Degree of Qn(x) ( n = 0,1,2,…)
C Output: QN(n) --- Qn(x)
C QD(n) --- Qn'(x)
C ====================================================
@@ -2828,10 +2828,10 @@
C
C =========================================================
C Purpose: Integrate [I0(t)-1]/t with respect to t from 0
-C to x, and K0(t)/t with respect to t from x to ì
-C Input : x --- Variable in the limits ( x ò 0 )
+C to x, and K0(t)/t with respect to t from x to ∞
+C Input : x --- Variable in the limits ( x ≥ 0 )
C Output: TTI --- Integration of [I0(t)-1]/t from 0 to x
-C TTK --- Integration of K0(t)/t from x to ì
+C TTK --- Integration of K0(t)/t from x to ∞
C =========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -2906,7 +2906,7 @@
C Routines called:
C (1) MSTA1 and MSTA2 for computing the starting
C point for backward recurrence
-C (2) GAM0 for computing gamma function (|x| ó 1)
+C (2) GAM0 for computing gamma function (|x| ≤ 1)
C =========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -3039,7 +3039,7 @@
C x --- Argument ( x > 0 )
C Output: HU --- U(a,b,z)
C ID --- Estimated number of significant digits
-C Routine called: GAMMA2 for computing â(x)
+C Routine called: GAMMA2 for computing Г(x)
C ======================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -3223,7 +3223,7 @@
C
C =========================================================
C Purpose : Compute the zeros of Laguerre polynomial Ln(x)
-C in the interval [0,ì], and the corresponding
+C in the interval [0,∞], and the corresponding
C weighting coefficients for Gauss-Laguerre
C integration
C Input : n --- Order of the Laguerre polynomial
@@ -3283,7 +3283,7 @@
C Output: PV --- Vv(x)
C Routines called:
C (1) DVLA for computing Dv(x) for large |x|
-C (2) GAMMA2 for computing â(x)
+C (2) GAMMA2 for computing Г(x)
C ===================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -3320,7 +3320,7 @@
C derivatives for a complex argument
C Input : z --- Complex argument
C v --- Order of Jv(z) and Yv(z)
-C ( v = n+v0, n = 0,1,2,..., 0 ó v0 < 1 )
+C ( v = n+v0, n = 0,1,2,..., 0 ≤ v0 < 1 )
C Output: CBJ(n) --- Jn+v0(z)
C CDJ(n) --- Jn+v0'(z)
C CBY(n) --- Yn+v0(z)
@@ -3576,7 +3576,7 @@
C derivatives for a complex argument
C Input : z --- Complex argument
C v --- Order of Jv(z) and Yv(z)
-C ( v = n+v0, n = 0,1,2,..., 0 ó v0 < 1 )
+C ( v = n+v0, n = 0,1,2,..., 0 ≤ v0 < 1 )
C Output: CBJ(n) --- Jn+v0(z)
C CDJ(n) --- Jn+v0'(z)
C CBY(n) --- Yn+v0(z)
@@ -3736,7 +3736,7 @@
C =======================================================
C Purpose: Compute Bessel functions J0(x), J1(x), Y0(x),
C Y1(x), and their derivatives
-C Input : x --- Argument of Jn(x) & Yn(x) ( x ò 0 )
+C Input : x --- Argument of Jn(x) & Yn(x) ( x ≥ 0 )
C Output: BJ0 --- J0(x)
C DJ0 --- J0'(x)
C BJ1 --- J1(x)
@@ -3862,13 +3862,13 @@
C
C ===================================================
C Purpose: Compute the incomplete gamma function
-C r(a,x), â(a,x) and P(a,x)
-C Input : a --- Parameter ( a ó 170 )
+C r(a,x), Г(a,x) and P(a,x)
+C Input : a --- Parameter ( a ≤ 170 )
C x --- Argument
C Output: GIN --- r(a,x)
-C GIM --- â(a,x)
+C GIM --- Г(a,x)
C GIP --- P(a,x)
-C Routine called: GAMMA2 for computing â(x)
+C Routine called: GAMMA2 for computing Г(x)
C ===================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -3915,7 +3915,7 @@
C =======================================================
C Purpose: Integrate Bessel functions I0(t) and K0(t)
C with respect to t from 0 to x
-C Input : x --- Upper limit of the integral ( x ò 0 )
+C Input : x --- Upper limit of the integral ( x ≥ 0 )
C Output: TI --- Integration of I0(t) from 0 to x
C TK --- Integration of K0(t) from 0 to x
C =======================================================
@@ -3980,7 +3980,7 @@
C =======================================================
C Purpose: Integrate modified Bessel functions I0(t) and
C K0(t) with respect to t from 0 to x
-C Input : x --- Upper limit of the integral ( x ò 0 )
+C Input : x --- Upper limit of the integral ( x ≥ 0 )
C Output: TI --- Integration of I0(t) from 0 to x
C TK --- Integration of K0(t) from 0 to x
C =======================================================
@@ -4055,7 +4055,7 @@
C and their derivatives
C Input : x --- Argument of Jv(x) and Yv(x)
C v --- Order of Jv(x) and Yv(x)
-C ( v = n+v0, 0 ó v0 < 1, n = 0,1,2,... )
+C ( v = n+v0, 0 ≤ v0 < 1, n = 0,1,2,... )
C Output: BJ(n) --- Jn+v0(x)
C DJ(n) --- Jn+v0'(x)
C BY(n) --- Yn+v0(x)
@@ -4245,7 +4245,7 @@
C =====================================================
C Purpose: Compute Bessel functions Jn(x), Yn(x) and
C their derivatives
-C Input : x --- Argument of Jn(x) and Yn(x) ( x ò 0 )
+C Input : x --- Argument of Jn(x) and Yn(x) ( x ≥ 0 )
C n --- Order of Jn(x) and Yn(x)
C Output: BJ(n) --- Jn(x)
C DJ(n) --- Jn'(x)
@@ -4363,7 +4363,7 @@
C
C =============================================
C Purpose: Compute Struve function H1(x)
-C Input : x --- Argument of H1(x) ( x ò 0 )
+C Input : x --- Argument of H1(x) ( x ≥ 0 )
C Output: SH1 --- H1(x)
C =============================================
C
@@ -4529,7 +4529,7 @@
C ==========================================================
C Purpose: Compute Bessel functions Jn(x) & Yn(x) and
C their derivatives
-C Input : x --- Argument of Jn(x) & Yn(x) ( x ò 0 )
+C Input : x --- Argument of Jn(x) & Yn(x) ( x ≥ 0 )
C n --- Order of Jn(x) & Yn(x)
C Output: BJ(n) --- Jn(x)
C DJ(n) --- Jn'(x)
@@ -4622,7 +4622,7 @@
C Output: DV(na) --- Dn+v0(x)
C DP(na) --- Dn+v0'(x)
C ( na = |n|, v0 = v-n, |v0| < 1,
-C n = 0,ñ1,ñ2,úúú )
+C n = 0,±1,±2,… )
C PDF --- Dv(x)
C PDD --- Dv'(x)
C Routines called:
@@ -4733,7 +4733,7 @@
C ===================================================
C Purpose: Evaluate the integral of Struve function
C H0(t) with respect to t from 0 and x
-C Input : x --- Upper limit ( x ò 0 )
+C Input : x --- Upper limit ( x ≥ 0 )
C Output: TH0 --- Integration of H0(t) from 0 and x
C ===================================================
C
@@ -4840,10 +4840,10 @@
SUBROUTINE GAMMA2(X,GA)
C
C ==================================================
-C Purpose: Compute gamma function â(x)
-C Input : x --- Argument of â(x)
-C ( x is not equal to 0,-1,-2,úúú)
-C Output: GA --- â(x)
+C Purpose: Compute gamma function Г(x)
+C Input : x --- Argument of Г(x)
+C ( x is not equal to 0,-1,-2,…)
+C Output: GA --- Г(x)
C ==================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -5058,7 +5058,7 @@
C ==================================================
C Purpose: Compute complete elliptic integrals K(k)
C and E(k)
-C Input : K --- Modulus k ( 0 ó k ó 1 )
+C Input : K --- Modulus k ( 0 ≤ k ≤ 1 )
C Output : CK --- K(k)
C CE --- E(k)
C ==================================================
@@ -5092,7 +5092,7 @@
C Purpose: Compute the incomplete beta function Ix(a,b)
C Input : a --- Parameter
C b --- Parameter
-C x --- Argument ( 0 ó x ó 1 )
+C x --- Argument ( 0 ≤ x ≤ 1 )
C Output: BIX --- Ix(a,b)
C Routine called: BETA for computing beta function B(p,q)
C ========================================================
@@ -5397,7 +5397,7 @@
C ==================================================
C Purpose: Compute complete and incomplete elliptic
C integrals F(k,phi) and E(k,phi)
-C Input : HK --- Modulus k ( 0 ó k ó 1 )
+C Input : HK --- Modulus k ( 0 ≤ k ≤ 1 )
C Phi --- Argument ( in degrees )
C Output : FE --- F(k,phi)
C EE --- E(k,phi)
@@ -5455,8 +5455,8 @@
C Purpose: Compute the elliptic integral of the third kind
C using Gauss-Legendre quadrature
C Input : Phi --- Argument ( in degrees )
-C k --- Modulus ( 0 ó k ó 1.0 )
-C c --- Parameter ( 0 ó c ó 1.0 )
+C k --- Modulus ( 0 ≤ k ≤ 1.0 )
+C c --- Parameter ( 0 ≤ c ≤ 1.0 )
C Output: EL3 --- Value of the elliptic integral of the
C third kind
C =========================================================
@@ -5576,7 +5576,7 @@
C b --- Parameter ( b <> 0,-1,-2,... )
C x --- Argument
C Output: HG --- M(a,b,x)
-C Routine called: GAMMA2 for computing â(x)
+C Routine called: GAMMA2 for computing Г(x)
C ===================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -5672,7 +5672,7 @@
C
C =============================================
C Purpose: Compute Struve function H0(x)
-C Input : x --- Argument of H0(x) ( x ò 0 )
+C Input : x --- Argument of H0(x) ( x ≥ 0 )
C Output: SH0 --- H0(x)
C =============================================
C
@@ -6322,7 +6322,7 @@
C
C ======================================================
C Purpose: Compute the integrals of Airy fnctions with
-C respect to t from 0 and x ( x ò 0 )
+C respect to t from 0 and x ( x ≥ 0 )
C Input : x --- Upper limit of the integral
C Output : APT --- Integration of Ai(t) from 0 and x
C BPT --- Integration of Bi(t) from 0 and x
@@ -6427,7 +6427,7 @@
C ========================================================
C Purpose: Compute modified Bessel functions In(x) and
C Kn(x), and their derivatives
-C Input: x --- Argument of In(x) and Kn(x) ( x ò 0 )
+C Input: x --- Argument of In(x) and Kn(x) ( x ≥ 0 )
C n --- Order of In(x) and Kn(x)
C Output: BI(n) --- In(x)
C DI(n) --- In'(x)
@@ -6796,7 +6796,7 @@
C ============================================================
C Purpose: Compute modified Bessel functions In(x) and Kn(x),
C and their derivatives
-C Input: x --- Argument of In(x) and Kn(x) ( 0 ó x ó 700 )
+C Input: x --- Argument of In(x) and Kn(x) ( 0 ≤ x ≤ 700 )
C n --- Order of In(x) and Kn(x)
C Output: BI(n) --- In(x)
C DI(n) --- In'(x)
@@ -6949,7 +6949,7 @@
C
C ===============================================================
C Purpose: Compute Mathieu functions cem(x,q) and sem(x,q)
-C and their derivatives ( q ò 0 )
+C and their derivatives ( q ≥ 0 )
C Input : KF --- Function code
C KF=1 for computing cem(x,q) and cem'(x,q)
C KF=2 for computing sem(x,q) and sem'(x,q)
@@ -7162,20 +7162,20 @@
SUBROUTINE FFK(KS,X,FR,FI,FM,FA,GR,GI,GM,GA)
C
C =======================================================
-C Purpose: Compute modified Fresnel integrals Fñ(x)
-C and Kñ(x)
-C Input : x --- Argument of Fñ(x) and Kñ(x)
+C Purpose: Compute modified Fresnel integrals F±(x)
+C and K±(x)
+C Input : x --- Argument of F±(x) and K±(x)
C KS --- Sign code
C KS=0 for calculating F+(x) and K+(x)
C KS=1 for calculating F_(x) and K_(x)
-C Output: FR --- Re[Fñ(x)]
-C FI --- Im[Fñ(x)]
-C FM --- |Fñ(x)|
-C FA --- Arg[Fñ(x)] (Degs.)
-C GR --- Re[Kñ(x)]
-C GI --- Im[Kñ(x)]
-C GM --- |Kñ(x)|
-C GA --- Arg[Kñ(x)] (Degs.)
+C Output: FR --- Re[F±(x)]
+C FI --- Im[F±(x)]
+C FM --- |F±(x)|
+C FA --- Arg[F±(x)] (Degs.)
+C GR --- Re[K±(x)]
+C GI --- Im[K±(x)]
+C GM --- |K±(x)|
+C GA --- Arg[K±(x)] (Degs.)
C ======================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -7616,7 +7616,7 @@
C Purpose: Compute complex parabolic cylinder function Dn(z)
C for large argument
C Input: z --- Complex argument of Dn(z)
-C n --- Order of Dn(z) (n = 0,ñ1,ñ2,úúú)
+C n --- Order of Dn(z) (n = 0,±1,±2,…)
C Output: CDN --- Dn(z)
C ===========================================================
C
@@ -7730,7 +7730,7 @@
C Purpose: Compute the associated Legendre function
C Pmv(x) with an integer order and an arbitrary
C nonnegative degree v
-C Input : x --- Argument of Pm(x) ( -1 ó x ó 1 )
+C Input : x --- Argument of Pm(x) ( -1 ≤ x ≤ 1 )
C m --- Order of Pmv(x)
C v --- Degree of Pmv(x)
C Output: PMV --- Pmv(x)
@@ -7826,15 +7826,15 @@
SUBROUTINE CGAMA(X,Y,KF,GR,GI)
C
C =========================================================
-C Purpose: Compute the gamma function â(z) or ln[â(z)]
+C Purpose: Compute the gamma function Г(z) or ln[Г(z)]
C for a complex argument
C Input : x --- Real part of z
C y --- Imaginary part of z
C KF --- Function code
-C KF=0 for ln[â(z)]
-C KF=1 for â(z)
-C Output: GR --- Real part of ln[â(z)] or â(z)
-C GI --- Imaginary part of ln[â(z)] or â(z)
+C KF=0 for ln[Г(z)]
+C KF=1 for Г(z)
+C Output: GR --- Real part of ln[Г(z)] or Г(z)
+C GI --- Imaginary part of ln[Г(z)] or Г(z)
C ========================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -8010,7 +8010,7 @@
C ===========================================================
C Purpose: Evaluate the integral H0(t)/t with respect to t
C from x to infinity
-C Input : x --- Lower limit ( x ò 0 )
+C Input : x --- Lower limit ( x ≥ 0 )
C Output: TTH --- Integration of H0(t)/t from x to infinity
C ===========================================================
C
@@ -8049,11 +8049,11 @@
SUBROUTINE LGAMA(KF,X,GL)
C
C ==================================================
-C Purpose: Compute gamma function â(x) or ln[â(x)]
-C Input: x --- Argument of â(x) ( x > 0 )
+C Purpose: Compute gamma function Г(x) or ln[Г(x)]
+C Input: x --- Argument of Г(x) ( x > 0 )
C KF --- Function code
-C KF=1 for â(x); KF=0 for ln[â(x)]
-C Output: GL --- â(x) or ln[â(x)]
+C KF=1 for Г(x); KF=0 for ln[Г(x)]
+C Output: GL --- Г(x) or ln[Г(x)]
C ==================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -8093,8 +8093,8 @@
C
C =====================================================
C Purpose: Compute Legendre functions Qn(x) and Qn'(x)
-C Input : x --- Argument of Qn(x) ( -1 ó x ó 1 )
-C n --- Degree of Qn(x) ( n = 0,1,2,úúú )
+C Input : x --- Argument of Qn(x) ( -1 ≤ x ≤ 1 )
+C n --- Degree of Qn(x) ( n = 0,1,2,… )
C Output: QN(n) --- Qn(x)
C QD(n) --- Qn'(x)
C ( 1.0D+300 stands for infinity )
@@ -8136,7 +8136,7 @@
C Output: PD --- Dv(x)
C Routines called:
C (1) VVLA for computing Vv(x) for large |x|
-C (2) GAMMA2 for computing â(x)
+C (2) GAMMA2 for computing Г(x)
C ====================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -8170,7 +8170,7 @@
C =========================================================
C Purpose: Compute modified Bessel functions I0(x), I1(1),
C K0(x) and K1(x), and their derivatives
-C Input : x --- Argument ( x ò 0 )
+C Input : x --- Argument ( x ≥ 0 )
C Output: BI0 --- I0(x)
C DI0 --- I0'(x)
C BI1 --- I1(x)
@@ -8280,7 +8280,7 @@
C Purpose: Compute the parabolic cylinder functions
C Dn(z) and Dn'(z) for a complex argument
C Input: z --- Complex argument of Dn(z)
-C n --- Order of Dn(z) ( n=0,ñ1,ñ2,úúú )
+C n --- Order of Dn(z) ( n=0,±1,±2,… )
C Output: CPB(|n|) --- Dn(z)
C CPD(|n|) --- Dn'(z)
C Routines called:
@@ -8373,7 +8373,7 @@
C =========================================================
C Purpose: Compute modified Bessel functions I0(x), I1(1),
C K0(x) and K1(x), and their derivatives
-C Input : x --- Argument ( x ò 0 )
+C Input : x --- Argument ( x ≥ 0 )
C Output: BI0 --- I0(x)
C DI0 --- I0'(x)
C BI1 --- I1(x)
@@ -8450,7 +8450,7 @@
C Input : p --- Parameter ( p > 0 )
C q --- Parameter ( q > 0 )
C Output: BT --- B(p,q)
-C Routine called: GAMMA2 for computing â(x)
+C Routine called: GAMMA2 for computing Г(x)
C ==========================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -8755,10 +8755,10 @@
SUBROUTINE PBWA(A,X,W1F,W1D,W2F,W2D)
C
C ======================================================
-C Purpose: Compute parabolic cylinder functions W(a,ñx)
+C Purpose: Compute parabolic cylinder functions W(a,±x)
C and their derivatives
-C Input : a --- Parameter ( 0 ó |a| ó 5 )
-C x --- Argument of W(a,ñx) ( 0 ó |x| ó 5 )
+C Input : a --- Parameter ( 0 ≤ |a| ≤ 5 )
+C x --- Argument of W(a,±x) ( 0 ≤ |x| ≤ 5 )
C Output : W1F --- W(a,x)
C W1D --- W'(a,x)
C W2F --- W(a,-x)
@@ -8963,7 +8963,7 @@
C Input: x --- Argument
C va --- Order
C Output: PD --- Dv(x)
-C Routine called: GAMMA2 for computing â(x)
+C Routine called: GAMMA2 for computing Г(x)
C ===================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -9050,7 +9050,7 @@
C
C =======================================================
C Purpose: Integrate Bessel functions J0(t) and Y0(t)
-C with respect to t from 0 to x ( x ò 0 )
+C with respect to t from 0 to x ( x ≥ 0 )
C Input : x --- Upper limit of the integral
C Output: TJ --- Integration of J0(t) from 0 to x
C TY --- Integration of Y0(t) from 0 to x
@@ -9264,8 +9264,8 @@
C ======================================================
C Purpose: Compute modified Struve function Lv(x) with
C an arbitrary order v
-C Input : v --- Order of Lv(x) ( |v| ó 20 )
-C x --- Argument of Lv(x) ( x ò 0 )
+C Input : v --- Order of Lv(x) ( |v| ≤ 20 )
+C x --- Argument of Lv(x) ( x ≥ 0 )
C Output: SLV --- Lv(x)
C Routine called: GAMMA2 to compute the gamma function
C ======================================================
@@ -9353,8 +9353,8 @@
C kind and their derivatives
C Input: x --- Argument of Riccati-Bessel function
C n --- Order of yn(x)
-C Output: RY(n) --- xúyn(x)
-C DY(n) --- [xúyn(x)]'
+C Output: RY(n) --- x·yn(x)
+C DY(n) --- [x·yn(x)]'
C NM --- Highest order computed
C ========================================================
C
@@ -9598,14 +9598,14 @@
C
C ======================================================
C Purpose: Compute confluent hypergeometric function
-C U(a,b,x) with integer b ( b = ñ1,ñ2,... )
+C U(a,b,x) with integer b ( b = ±1,±2,... )
C Input : a --- Parameter
C b --- Parameter
C x --- Argument
C Output: HU --- U(a,b,x)
C ID --- Estimated number of significant digits
C Routines called:
-C (1) GAMMA2 for computing gamma function â(x)
+C (1) GAMMA2 for computing gamma function Г(x)
C (2) PSI_SPEC for computing psi function
C ======================================================
C
@@ -10052,8 +10052,8 @@
C
C =====================================================
C Purpose: Compute Bessel functions Jn(x) and their
-C first and second derivatives ( n= 0,1,úúú )
-C Input: x --- Argument of Jn(x) ( x ò 0 )
+C first and second derivatives ( n= 0,1,… )
+C Input: x --- Argument of Jn(x) ( x ≥ 0 )
C n --- Order of Jn(x)
C Output: BJ(n+1) --- Jn(x)
C DJ(n+1) --- Jn'(x)
@@ -10097,7 +10097,7 @@
C Purpose: Compute spherical Bessel functions jn(x) and
C their derivatives
C Input : x --- Argument of jn(x)
-C n --- Order of jn(x) ( n = 0,1,úúú )
+C n --- Order of jn(x) ( n = 0,1,… )
C Output: SJ(n) --- jn(x)
C DJ(n) --- jn'(x)
C NM --- Highest order computed
@@ -10289,7 +10289,7 @@
C Input : m --- Mode parameter, m = 0,1,2,...
C n --- Mode parameter, n = m,m+1,m+2,...
C c --- Spheroidal parameter
-C x --- Argument (x ò 0)
+C x --- Argument (x ≥ 0)
C cv --- Characteristic value
C KF --- Function code
C KF=1 for the first kind
@@ -10404,7 +10404,7 @@
C ======================================================
C Purpose: Compute the zeros of Bessel functions Jn(x),
C Yn(x), and their derivatives
-C Input : n --- Order of Bessel functions ( n ó 101 )
+C Input : n --- Order of Bessel functions ( n ≤ 101 )
C NT --- Number of zeros (roots)
C Output: RJ0(L) --- L-th zero of Jn(x), L=1,2,...,NT
C RJ1(L) --- L-th zero of Jn'(x), L=1,2,...,NT
@@ -10485,9 +10485,9 @@
C =======================================================
C Purpose: Compute modified Bessel functions Iv(x) and
C Kv(x), and their derivatives
-C Input : x --- Argument ( x ò 0 )
+C Input : x --- Argument ( x ≥ 0 )
C v --- Order of Iv(x) and Kv(x)
-C ( v = n+v0, n = 0,1,2,..., 0 ó v0 < 1 )
+C ( v = n+v0, n = 0,1,2,..., 0 ≤ v0 < 1 )
C Output: BI(n) --- In+v0(x)
C DI(n) --- In+v0'(x)
C BK(n) --- Kn+v0(x)
@@ -10759,7 +10759,7 @@
C and modified Bessel functions Iv(x) and
C Kv(x), and their derivatives with v=1/3,2/3
C Input : x --- Argument of Jv(x),Yv(x),Iv(x) and
-C Kv(x) ( x ò 0 )
+C Kv(x) ( x ≥ 0 )
C Output: VJ1 --- J1/3(x)
C VJ2 --- J2/3(x)
C VY1 --- Y1/3(x)
@@ -10930,7 +10930,7 @@
C complex argument
C Input : z --- Complex argument z
C v --- Real order of Iv(z) and Kv(z)
-C ( v =n+v0, n = 0,1,2,..., 0 ó v0 < 1 )
+C ( v =n+v0, n = 0,1,2,..., 0 ≤ v0 < 1 )
C Output: CBI(n) --- In+v0(z)
C CDI(n) --- In+v0'(z)
C CBK(n) --- Kn+v0(z)
@@ -11091,7 +11091,7 @@
C complex argument
C Input : z --- Complex argument
C v --- Real order of Iv(z) and Kv(z)
-C ( v = n+v0, n = 0,1,2,úúú, 0 ó v0 < 1 )
+C ( v = n+v0, n = 0,1,2,…, 0 ≤ v0 < 1 )
C Output: CBI(n) --- In+v0(z)
C CDI(n) --- In+v0'(z)
C CBK(n) --- Kn+v0(z)
@@ -11401,8 +11401,8 @@
C kind and their derivatives
C Input: x --- Argument of Riccati-Bessel function
C n --- Order of jn(x) ( n = 0,1,2,... )
-C Output: RJ(n) --- xújn(x)
-C DJ(n) --- [xújn(x)]'
+C Output: RJ(n) --- x·jn(x)
+C DJ(n) --- [x·jn(x)]'
C NM --- Highest order computed
C Routines called:
C MSTA1 and MSTA2 for computing the starting
@@ -11458,7 +11458,7 @@
C
C ========================================================
C Purpose : Compute the zeros of Hermite polynomial Ln(x)
-C in the interval [-ì,ì], and the corresponding
+C in the interval [-∞,∞], and the corresponding
C weighting coefficients for Gauss-Hermite
C integration
C Input : n --- Order of the Hermite polynomial
@@ -11528,7 +11528,7 @@
C =======================================================
C Purpose: Compute Bessel functions J0(x), J1(x), Y0(x),
C Y1(x), and their derivatives
-C Input : x --- Argument of Jn(x) & Yn(x) ( x ò 0 )
+C Input : x --- Argument of Jn(x) & Yn(x) ( x ≥ 0 )
C Output: BJ0 --- J0(x)
C DJ0 --- J0'(x)
C BJ1 --- J1(x)
@@ -11661,7 +11661,7 @@
C =====================================================
C Purpose: Compute modified spherical Bessel functions
C of the second kind, kn(x) and kn'(x)
-C Input : x --- Argument of kn(x) ( x ò 0 )
+C Input : x --- Argument of kn(x) ( x ≥ 0 )
C n --- Order of kn(x) ( n = 0,1,2,... )
C Output: SK(n) --- kn(x)
C DK(n) --- kn'(x)
@@ -11701,7 +11701,7 @@
C
C ============================================
C Purpose: Compute exponential integral En(x)
-C Input : x --- Argument of En(x) ( x ó 20 )
+C Input : x --- Argument of En(x) ( x ≤ 20 )
C n --- Order of En(x)
C Output: EN(n) --- En(x)
C Routine called: E1XB for computing E1(x)
@@ -11726,9 +11726,9 @@
SUBROUTINE GAIH(X,GA)
C
C =====================================================
-C Purpose: Compute gamma function â(x)
-C Input : x --- Argument of â(x), x = n/2, n=1,2,úúú
-C Output: GA --- â(x)
+C Purpose: Compute gamma function Г(x)
+C Input : x --- Argument of Г(x), x = n/2, n=1,2,…
+C Output: GA --- Г(x)
C =====================================================
C
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
@@ -11759,7 +11759,7 @@
C Output: VV(na) --- Vv(x)
C VP(na) --- Vv'(x)
C ( na = |n|, v = n+v0, |v0| < 1
-C n = 0,ñ1,ñ2,úúú )
+C n = 0,±1,±2,… )
C PVF --- Vv(x)
C PVD --- Vv'(x)
C Routines called:
@@ -11881,8 +11881,8 @@
C complex argument
C Input : x --- Real part of z
C y --- Imaginary part of z
-C m --- Order of Qmn(z) ( m = 0,1,2,úúú )
-C n --- Degree of Qmn(z) ( n = 0,1,2,úúú )
+C m --- Order of Qmn(z) ( m = 0,1,2,… )
+C n --- Degree of Qmn(z) ( n = 0,1,2,… )
C mm --- Physical dimension of CQM and CQD
C Output: CQM(m,n) --- Qmn(z)
C CQD(m,n) --- Qmn'(z)
@@ -12270,7 +12270,7 @@
C KC=3 for computing both the first
C and second kinds
C m --- Order of Mathieu functions
-C q --- Parameter of Mathieu functions ( q ò 0 )
+C q --- Parameter of Mathieu functions ( q ≥ 0 )
C x --- Argument of Mathieu functions
C Output: F1R --- Mcm(1)(x,q) or Msm(1)(x,q)
C D1R --- Derivative of Mcm(1)(x,q) or Msm(1)(x,q)
@@ -12575,8 +12575,8 @@
C ======================================================
C Purpose: Compute spherical Bessel functions yn(x) and
C their derivatives
-C Input : x --- Argument of yn(x) ( x ò 0 )
-C n --- Order of yn(x) ( n = 0,1,úúú )
+C Input : x --- Argument of yn(x) ( x ≥ 0 )
+C n --- Order of yn(x) ( n = 0,1,… )
C Output: SY(n) --- yn(x)
C DY(n) --- yn'(x)
C NM --- Highest order computed
@@ -12621,7 +12621,7 @@
C Purpose: Compute Jacobian elliptic functions sn u, cn u
C and dn u
C Input : u --- Argument of Jacobian elliptic fuctions
-C Hk --- Modulus k ( 0 ó k ó 1 )
+C Hk --- Modulus k ( 0 ≤ k ≤ 1 )
C Output : ESN --- sn u
C ECN --- cn u
C EDN --- dn u
@@ -12662,8 +12662,8 @@
C =====================================================
C Purpose: Compute Struve function Hv(x) with an
C arbitrary order v
-C Input : v --- Order of Hv(x) ( -8.0 ó v ó 12.5 )
-C x --- Argument of Hv(x) ( x ò 0 )
+C Input : v --- Order of Hv(x) ( -8.0 ≤ v ≤ 12.5 )
+C x --- Argument of Hv(x) ( x ≥ 0 )
C Output: HV --- Hv(x)
C Routine called: GAMMA2 to compute the gamma function
C =====================================================
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