All Questions

I have an integral of the form $$ \int_R^{\infty} e^{-x} x^n \vert L_m^{\alpha}(x) \vert^2 \ dx,$$ where $L_m^{\alpha}$ is the generalized Laguerre polynomial and $n \ge 0.$ I would to get a nice ...

I would like to understand how approximations by monomials and approximations by other kinds of functions are related which I illustrate with an example. Consider the interval $[-\pi,\pi]$ let's say. ...

I wonder whether the following integral of Airy functions can be computed? \begin{equation} F(x,y):=\int_{-\infty}^\infty \int_{-\infty}^\infty Ai(x-u)Ai(y-v) e^{ituv}du dv,\quad t \in \mathbb R. \end{...

For a research problem I am working on in PDE, I need to obtain asymptotics for the counting function of $$\{0<\alpha <\lambda: \exists n\in \mathbb{N} \textrm{ such that }J_n(\alpha)=0 \textrm{ ...