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Results tagged with special-functions
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user 8135
Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.
1
vote
0
answers
94
views
Sufficient conditions for sums of Laguerre polynomials to be non-negative
I am interested in sufficient conditions on non-negative sequences of coefficients $\{c_{2n}\}_{n\ge 0}$ guaranteeing that
$$%\begin{equation}\label{cond}
\sum_{n=0}^\infty c_{2n} L_{2n}^{(1)}(x)\ge 0 …
- 650
4
votes
1
answer
339
views
Integral operator with Bessel kernel
For $x,y\ge 0$, let
$$
k(x,y)= \frac {J_1(2\sqrt{xy})}{\sqrt{xy}},
$$
where $J_1$ is the the Bessel function of the first kind
$$
J_{1}(z)=\sum_{k=0}^{\infty}(-1)^{k} \frac{\left(\frac{z}{2}\right)^{2 …
- 650