Elliptic Faulhaber polynomials and Lame densities of states

DOI10.1155/IMRN/2006/62120zbMath1142.37042arXivmath-ph/0508066OpenAlexW1980184288MaRDI QIDQ3428117

Marie-Pierre Grosset, Alexander P. Veselov

Publication date: 27 March 2007

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0508066

zbMATH Keywords

solitonsKdV equationWeierstrass elliptic functionFaulhaber polynomials

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Lamé, Mathieu, and spheroidal wave functions (33E10)

Related Items (10)

On the spectra of real and complex Lamé operators ⋮ Quantum geometry from the toroidal block ⋮ The toroidal block and the genus expansion ⋮ A new tau method for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation ⋮ On the large \(\omega\)-deformations in the Nekrasov-Shatashvili limit of \( \mathcal{N}={2}^{*} \) SYM ⋮ Unnamed Item ⋮ On Appell sequences of polynomials of Bernoulli and Euler type ⋮ Root asymptotics of spectral polynomials for the Lamé operator ⋮ Faulhaber's theorem on power sums ⋮ Effective gravitational couplings of four-dimensional \(\mathcal{N} = 2\) supersymmetric gauge theories

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