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I am looking for a power series representation of $$ \frac{1}{K_{\nu}(x)}, $$ where $K_{\nu}$ denotes the modified Bessel function of the second kind and $\nu>-1/2$ is not an integer. I know that ...

Is there a formulas for the following integral $$\int^\infty_0 e^{-ar^2}L^1_k(b r^2)J_1(cr)r^d dr $$ where $L^1_k$ is the Laguerre polynomials of type 1 and $J_1$ is the Bessel function with $a,...

I encounter the following integral when trying to find the inverse Fourier transform of the characteristic function of a certain sum of random variables. Here, $0\le\lambda\le1$, $p\ge0$, $q\ge0$ are ...

I encounter the following integral when trying to find the inverse Fourier transform of the characteristic function of a certain sum of random variables. Here, $p\ge0$, $q\ge0$ are real, and $n,a,b$ ...

I have asked similar questions on Math Stack Exchange, but not been able to receive many helpful responses. Therefore, I am posting this problem here, and any input would be extremely valuable. I ...

I would like to preface this question by saying that I have asked a series of questions on this topic on Math Stack Exchange, but have almost never received any fruitful responses, with the exception ...