Asymptotic expansion of Mellin transform of products of modified Bessel function K

Let n1 be an integer, let


for x,y0.

When n=1, this is just Mellin transform of the Bessel K function. When n=2, F(x,y) has an explicit form in product of Gamma functions, given by the Parseval formula for Mellin transform.

For general n, I expect some Stirling formula type estimation for F(x,y). I tried with Laplace method but didn’t get anywhere.


Source : Link , Question Author : Ted Mao , Answer Author : Community

Leave a Comment