apply python's sympy function in mathematica

Question

I recently try this $$\int\frac{\mathop{\rm Si}(x)}x\,dx$$

Mathematica failed to calculate it.

Integrate[SinIntegral[x]/x, x]

Mma 11.3 failed,but 12.0 can do it.

Sympy gives the answer

from sympy import *
x = symbols("x")
print(integrate(Si(x)/x, x))

x*hyper((1/2, 1/2), (3/2, 3/2, 3/2), -x**2/4)

So I wanted to use the result in Mma.

I have searched in sympy's document,but still can't find solution.

How can I directly get this function in mathematica?

I saw numpy can be used as follows:(add import numpy as np to the beginning,otherwise it will return wrong)

Which maybe helpful.

Add:

12.0 will return an object.But I temporaily don't know how to use it.(picture is from others)

Mathematica 12.0 can solve this integral... So why use SymPy? — ktm, Jan 07 '20 at 14:51
@user6014 because it's useful to put several tools together. Besides,I temporarily use 11.3. — AsukaMinato, Jan 07 '20 at 15:24
@user6014 Some users may not have access to Mathematica 12.0 yet either, unfortunately. It can be quite expensive. — Michael A, Jan 07 '20 at 15:31
Are you interested in sympy-based solutions that work only in Mathematica 12.0? Mathematica's Python interface became much better in 12.0. — Szabolcs, Jan 08 '20 at 08:31
@Szabolcs ，So it's very interesting. 11.3 can't solve it, but 12.0 can. 11.3 can't interface with python well, but 12.0 can.Seems the solution is to upgrade to 12.0. — AsukaMinato, Jan 08 '20 at 09:18

score 3 · Accepted Answer · answered Jan 08 '20 at 09:18

3

As an alternative, you may use Rubi:

Get["Rubi`"]
Int[SinIntegral[x]/x, x]

1/2 x HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, -I x] + 1/2 x HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, I x]

answered Jan 08 '20 at 09:18

yarchik

1

so it seems like this: 11.3 use Rubi can solve it. 12.0 can solve it directly. 12.0 can also use sympy to solve it. – AsukaMinato Jan 08 '20 at 09:33

1 Answers1