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How can I derive the formula which converts the product of Bessel function of the second kind and the sine function into Meijer $G$-function,

$$ \sin(\sqrt{z})Y_v(\sqrt{z})=\frac{1}{\sqrt{2}}G_{3,5}^{2,2} \left( z\left| \begin{matrix}1/4,3/4,-v/2\\ (v+1)/2,(1-v)/2,-v/2,-v/2,v/2 \end{matrix}\right.\right). $$

Thanks.

Nosrati
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mywyk5522
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  • You can reduce that formula to an identity involving hypergeometric functions by the same method as here. The G-function becomes a sum of two ${_2F_3}$ functions. – Maxim Aug 25 '18 at 17:17

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