It does not have an anti-derivative in terms of elementary functions. You could do a series expansion and integrate each term. Note that this is the numpy mailing list. The sympy mailing list is to be found at http://sympy.org/en/support.html Sameer On 11 March 2012 12:36, aa <telukpalu@gmail.com> wrote:
why sympy cannot integrate sin(x**2)?? _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Can you? The question should be: Why sympy does not have Fresnel integrals? On Sun, Mar 11, 2012 at 1:06 AM, aa <telukpalu@gmail.com> wrote:
why sympy cannot integrate sin(x**2)?? _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Le dimanche 11 mars 2012 à 01:31 -0600, Val Kalatsky a écrit :
Can you? The question should be: Why sympy does not have Fresnel integrals?
Well, the development version has hypergeometric functions, which is enough to integrate sin(x**2):
from sympy import * x = Symbol('x') integrate(sin(x**2)) x**3*gamma(3/4)*hyper((3/4,), (3/2, 7/4), -x**4/4)/(4*gamma(7/4)) integrate(sin(x**2), (x, 0, oo)) sqrt(2)*sqrt(pi)/4
f = lambdify(x, integrate(sin(x**2))) f(4567.) mpf('0.62676518399179759') f(np.linspace(-5., 5., 10)) Traceback (most recent call last): File "<ipython-input-35-97e0996f77c3>", line 1, in <module> f(np.linspace(-5., 5., 10)) File "<string>", line 1, in <lambda> File "/home/ronan/dev/sympy/sympy/mpmath/functions/hypergeometric.py",
It can also create a numerical function for the result, but it uses mpmath, so it won't play well with numpy: line 199, in hyper z = ctx.convert(z) File "/home/ronan/dev/sympy/sympy/mpmath/ctx_mp_python.py", line 662, in convert return ctx._convert_fallback(x, strings) File "/home/ronan/dev/sympy/sympy/mpmath/ctx_mp.py", line 556, in _convert_fallback raise TypeError("cannot create mpf from " + repr(x)) TypeError: cannot create mpf from array([ -1.56250000e+02, -5.71797363e +01, -1.48843545e+01, -1.92901235e+00, -2.38149672e-02, -2.38149672e-02, -1.92901235e+00, -1.48843545e+01, -5.71797363e+01, -1.56250000e+02])
On Sun, Mar 11, 2012 at 1:06 AM, aa <telukpalu@gmail.com> wrote: why sympy cannot integrate sin(x**2)?? _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
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Val Kalatsky