# How to compute this integral numerically.

Is there a way to compute the following integral numerically?,

$\int_0^{\infty}\left(-\frac{2 x \Gamma \left(\frac{1}{4}\right) \, _1F_3\left(\frac{1}{4};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x^4}{256}\right)}{\sqrt{\pi }}+x^2 \, _1F_3\left(\frac{1}{2};\frac{3}{4},\frac{5}{4},\frac{3}{2};\frac{x^4}{256}\right)+\sqrt{\frac{2}{\pi }} \Gamma \left(\frac{1}{4}\right) \Gamma \left(\frac{3}{4}\right)\right)dx$

We know that $-\frac{2 x \Gamma \left(\frac{1}{4}\right) \, _1F_3\left(\frac{1}{4};\frac{1}{2},\frac{3}{4},\frac{5}{4};\frac{x^4}{256}\right)}{\sqrt{\pi }}+x^2 \, _1F_3\left(\frac{1}{2};\frac{3}{4},\frac{5}{4},\frac{3}{2};\frac{x^4}{256}\right) \rightarrow -\sqrt{\frac{2}{\pi }} \Gamma \left(\frac{1}{4}\right) \Gamma \left(\frac{3}{4}\right)$ as $x \rightarrow \infty.$

• Mathematica could not handle to compute this integral – Dilruk Gallage Jul 20 '17 at 6:16
• What is $g(x)$? Is it $F_3$? – MathArt Jul 20 '17 at 6:26
• Could you post the Mathematica syntax since, being almost blind, I have serious problems to read it ? I should try with other tools. – Claude Leibovici Jul 20 '17 at 6:26
• $g(x)$ is the integrand – Dilruk Gallage Jul 20 '17 at 6:40
• The integral is zero. Indeed the value from 0 to 1 is almost identical to the opposite of the value from 0 to 20. The "tail" from 20 on is almost zero – Raffaele Jul 20 '17 at 10:29