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Oleg Marichev

[R&DL] Wolfram R&D LIVE: Ask Integration Questions to Oleg Marichev

Oleg Marichev, Wolfram Research Inc
Posted 2 months ago
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MODERATOR NOTE: This is the notebook used in the livestream "Ask Integration Questions to Oleg Marichev" on Wednesday, January 25 -- a part of Wolfram R&D livestream series announced and scheduled here: https://wolfr.am/RDlive For questions about this livestream, please leave a comment below.
POSTED BY: Oleg Marichev
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For this integral:

$$\int_1^0 \pmb{H}_0\left(\sqrt{1-z^2} z\right) \, dz=\frac{2 \, _2F_3\left(1,1;\frac{5}{4},\frac{3}{2},\frac{7}{4};-\frac{1}{16}\right)}{3 \pi }$$

we use a Mellin Transform to solve:

   InverseMellinTransform[
      Integrate[
       MellinTransform[StruveH[0, A*Sqrt[1 - z^2] z], A, s], {z, 0, 1}, 
       Assumptions -> s < 1], s, A] /. A -> 1 // FullSimplify

   (*(2 HypergeometricPFQ[{1, 1}, {5/4, 3/2, 7/4}, -(1/16)])/(3 \[Pi])*)

Regards M.I.
POSTED BY: Mariusz Iwaniuk

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