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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
4
votes
Accepted
Extremizing sequence consists of two elements
The question is very easy.
Indeed, put $\gamma=\gamma(X,\lambda)$ and $S=\sum_{m \in I} e^{-\gamma x_m}$.
The equality
$$ \sum_{m \in I} (\lambda-x_m) e^{-\gamma x_m}=0$$
implies
$$\lambda S=\sum_{m \ …