Proof of converting the product of Bessel function of the second kind and the sine function into Meijer $G$-function.

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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,




$$
sin(sqrtz)Y_v(sqrtz)=frac1sqrt2G_3,5^2,2 left( zleft| beginmatrix1/4,3/4,-v/2\ (v+1)/2,(1-v)/2,-v/2,-v/2,v/2 endmatrixright.right).
$$




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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 at 17:17














up vote
3
down vote

favorite












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,




$$
sin(sqrtz)Y_v(sqrtz)=frac1sqrt2G_3,5^2,2 left( zleft| beginmatrix1/4,3/4,-v/2\ (v+1)/2,(1-v)/2,-v/2,-v/2,v/2 endmatrixright.right).
$$




Thanks.







share|cite|improve this question














migrated from mathematica.stackexchange.com Aug 25 at 11:11


This question came from our site for users of Wolfram Mathematica.














  • 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 at 17:17












up vote
3
down vote

favorite









up vote
3
down vote

favorite











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,




$$
sin(sqrtz)Y_v(sqrtz)=frac1sqrt2G_3,5^2,2 left( zleft| beginmatrix1/4,3/4,-v/2\ (v+1)/2,(1-v)/2,-v/2,-v/2,v/2 endmatrixright.right).
$$




Thanks.







share|cite|improve this question














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,




$$
sin(sqrtz)Y_v(sqrtz)=frac1sqrt2G_3,5^2,2 left( zleft| beginmatrix1/4,3/4,-v/2\ (v+1)/2,(1-v)/2,-v/2,-v/2,v/2 endmatrixright.right).
$$




Thanks.









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edited Aug 25 at 17:21









Nosrati

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asked Aug 25 at 2:44









mywyk5522

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migrated from mathematica.stackexchange.com Aug 25 at 11:11


This question came from our site for users of Wolfram Mathematica.






migrated from mathematica.stackexchange.com Aug 25 at 11:11


This question came from our site for users of Wolfram Mathematica.













  • 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 at 17:17
















  • 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 at 17:17















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 at 17:17




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 at 17:17















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