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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
16
votes
Accepted
Majorization and Schur Polynomials
This question is listed as a conjecture (conjecture 7.4 in the section "Open questions") in a recent paper of Cuttler, Greene and Skandera.
5
votes
An elementary proof for a limit?
Adapting Fedor's argument, we have
$$
a_n-a_{n-1}=\frac{1}{n\log(n)}+\log\log(n-1)-\log\log n=
\frac{1}{n\log(n)}+\log\left(\frac{\log(n-1)}{\log n}\right),
$$
and, similarly to the calculation from …