I think you advised about the code which is the same appearance. ========================================================================== Problem is not here Sir.... I will give you exactly what I was talking about. I have ready codes already(It would be kind of you if you checked the following codes, may be): ------------------------------------------------------------------------------------------------------------------------------ ## Bessel function of the first kind # mathematical form: Jn(x)--> n=arg1, x=arg2 # returns --> Jn(x) value in a complex form ------------------------------ def bes_1(arg1,arg2): nu=arg1+0.5 # nu=n+0.5: Jn(x) --> Jnu(x) return sqrt(pi/(2*arg2))*np.round(jv(nu,arg2),5) # jv(nu,arg2)--> from 'numpy.special' in PYTHON -------------------------------------------------------------------------------------------------------------------------------- ## Bessel function of the second kind # mathematical form: Yn(x)--> n=arg1, x=arg2 # returns --> Yn(x) value in a complex form --------------------------------- def bes_2 ( arg1, arg2 ): nu = arg1 + 0.5 # nu=n+0.5: Yn(x)--> Ynu(x) return sqrt ( pi / ( 2 * arg2 ) ) * np.round ( yv ( nu , arg2 ) , 5) # yv(nu,arg2)--> from 'numpy.special' in PYTHON --------------------------------- ------------------------------------------------------------------------------------------------------- ## Hankel function of the first kind # mathematical form: Hn(x)= Jn(x)+Yn(x)j # returns --> Hn(x) value in a complex form --------------------------------- def hank_1 ( arg1, arg2 ): return bes_1 ( arg1 , arg2 ) + bes_2 ( arg1 , arg2 ) * 1.0j # Hn(x)= Jn(x)+Yn(x)j ------------------------------------------------------------------------------------------------------------------------------------------- ## Bessel function of the first kind derivative # mathematical form: d(z*jn(z))=z*jn-1(z)-n*jn(z) where, z=x or m*x --------------------------------- def bes_der1 ( arg1 , arg2 ): return arg2 * bes_1 ( arg1 - 1, arg2 ) - arg1 * bes_1 ( arg1 , arg2 ) --------------------------------------------------------------------------------------------------------------------------------------------- ## Hankel function of the first kind derivative # mathematical form: d(z*hankeln(z))=z*hankeln-1(z)-n*hankeln(z) where, z=x or m*x def hank_der1 ( arg1 , arg2 ): return arg2 * hank_1 ( arg1 - 1, arg2 ) - arg1 * hank_1( arg1, arg2 ) --------------------------------------------------------------------------------------------------------------------------------------------- FOR MY CASE: m = 2513.2741228718346 + 201.0619298974676j x = 502.6548245743669 def F(m,x): nmax = x + 2.0 + 4.0 * x ** ( 1.0 / 3.0 ) # nmax= gives 536.0 as expected value nstop = np.round( nmax ) n = np.arange ( 0.0 ,nstop, dtype = float) z = m * x m2 = m * m val1 = m2 * bes_1 ( en , z ) * bes_der1 ( en, x) val2 = bes_1 ( en , x ) * bes_der1 ( en , z ) val3 = m2 * bes_1 ( en , z ) * hank_der1 ( en , x ) val4 = hank_1 ( en , x ) * bes_der1 ( en , z ) an = ( val1 - val2 ) / ( val3 - val4 ) val5 = bes_1 ( en , z ) * bes_der1 ( en, x ) val6 = bes_1 ( en , x ) * bes_der1 ( en, z ) val7 = bes_1 ( en , z ) * hank_der1 ( en, x ) val8 = hank_1 ( en , x ) * bes_der1 ( en , z ) bn = ( val5 - val6 ) / ( val7 - val8 ) return an, bn !!!! PROBLEM IS RETURNING THE an, bn at a given value which I showed before F(m,x) function WHAT IS WRONG WITH THIS?????? Пятница, 21 декабря 2012, 13:59 от Pauli Virtanen <pav@iki.fi>:
Dag Sverre Seljebotn <d.s.seljebotn <at> astro.uio.no> writes: [clip]
Do you have an implemention of the Bessel functions that work as you wish in C or Fortran? If so, that could be wrapped and called from Python.
For spherical Bessel functions it's possible to also use the relation to Bessel functions, which have a better implementation (AMOS) in Scipy:
import numpy as np from scipy.special import jv
def sph_jn(n, z): return jv(n + 0.5, z) * np.sqrt(np.pi / (2 * z))
print sph_jn(536, 2513.2741228718346 + 201.0619298974676j) # (2.5167666386507171e+81+3.3576357192536334e+81j)
This should solve the problem.
-- Pauli Virtanen
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