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,
$$
sin(sqrtz)Y_v(sqrtz)=frac1sqrt2G_3,5^2,2 left( zleft| beginmatrix1/4,3/4,-v/2\ (v+1)/2,(1-v)/2,-v/2,-v/2,v/2 endmatrixright.right).
$$
Thanks.
special-functions
migrated from mathematica.stackexchange.com Aug 25 at 11:11
This question came from our site for users of Wolfram Mathematica.
add a comment |Â
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.
special-functions
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.
â Maxim
Aug 25 at 17:17
add a comment |Â
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.
special-functions
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.
special-functions
edited Aug 25 at 17:21
Nosrati
21.5k41746
21.5k41746
asked Aug 25 at 2:44
mywyk5522
161
161
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.
â Maxim
Aug 25 at 17:17
add a comment |Â
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.
â 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.
â 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.
â Maxim
Aug 25 at 17:17
add a comment |Â
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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.
â Maxim
Aug 25 at 17:17