Borwein integrals

[jma...@gmail.com]

Hello

I wanted to calculate the Borwein integrals using sympy.
For some integrals, sympy provides the correct result
but for an other one it seems crashed.

Here my code:

>>> from sympy import *
>>> from operator import mul
>>> from functools import reduce

>>> x = symbols("x")
>>> f = lambda n: reduce(mul, (sin(x/k)/(x/k) for k in range(1, n+2, 2)))

>>> f(1)
sin(x)/x

>>> f(3)
3*sin(x/3)*sin(x)/x**2

>>> f(5)
15*sin(x/5)*sin(x/3)*sin(x)/x**3

>>> integrate(f(1), (x, 0, oo))
pi/2     CORRECT

>>> integrate(f(3), (x, 0, oo))
pi/2    CORRECT

>>> integrate(f(5), (x, 0, oo))

NO RESULT
python shell seems stuck, I have to stop it
after few minutes with a ctrl C


Regards

[Aaron Meurer]

SymPy doesn't know how to compute the integral. It is getting stuck in
a heuristic integrator that runs after all the other algorithms, which
often does this (we would like to remove it eventually). If you left
it long enough, it would return, but it would just give an unevaluated
integral.

Aaron Meurer

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