# Questions tagged [bessel-functions]

Questions related to Bessel functions.

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### Do we lose orthogonality of Bessel functions when we change interval

This is the basic definition of integral when you calculate integral product of orthogonal Bessel functions. What happens when you change integral bounds from [0,a] to [b,c]? Do you lose the ...
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### How to prove that this series of functions converges uniformly?

Let $z_0 \in \mathbb{C} \setminus \{0\}$ be a fixed complex number and let $z \in \mathbb{C}$. Let $K \subset \mathbb{C}$ be a compact set. I'm trying to use the Weiertrass $M$ - test to show that the ...
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### A simple(maybe not as it looks) integration

I am stuck with a simple-looking integral: $\int_0^\infty dx \sqrt {x^2+M^2} \cdot e^{-x}$ where $M$ is just a real constant. I thought it could be expressed with the Modified Bessel Function, but it ...
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### For what reason Bessel functions of the first kind can be differenciated in relation to the variable $q$?

For that reason the modified bessel function $I_q(\rho)$ defined as $$I_{q}(\rho)=\sum_{m=0}^{\infty}\frac{(\rho/2)^{2m+q}}{m!\Gamma(m+q+1)},$$ where in the above $\rho$ is fixed, can be ...