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Results tagged with ca.classical-analysis-and-odes
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user 8135
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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
$$%\begin{equation}\label{cond}
\sum_{n=0}^\infty c_{2n} L_{2n}^{(1)}(x)\ge 0 …
- 650
4
votes
0
answers
246
views
Legendre-Fenchel transform
Suppose $F:\mathbb R^n\to \mathbb R$ is a convex continuous function.
Moreover, for any $x\in \mathbb R^n$,
$$
\limsup_{\lambda\to\infty} \frac {|F(\lambda x)|}{\lambda}<\infty.
$$
I would like to con …
- 650