Use Meijer-G function to represent the products of two Bessel functions

258 Views Asked by At

Here I define two modified Bessel functions of the second type: $K_{\mu }\sqrt{az}$, $K_{v} \sqrt{\frac {b}{z}}$. I am struggling to represent the products of these two modified bessel functions by Meijer-G functions. I try two ways. The fisrt way is to obtain the Meijer-G function representations of two bessel functions seperately and then multiply the two Meijer-G functions. Howerer, I can not found the Meijer-G function representation of $K_{v} \sqrt{\frac {b}{z}}$. The second way is to directly obtain the Meijer-G function representation of the $K_{\mu }\sqrt{az} K_{v} \sqrt{\frac {b}{z}}$.However, I am struggling to obtain the products by Meijer-G function. Do you have any ideas?