Displaying similar documents to “A simple solution to Basel problem.”

Some sums of Legendre and Jacobi polynomials

Jan Gustavsson (2001)

Mathematica Bohemica

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We prove identities involving sums of Legendre and Jacobi polynomials. The identities are related to Green’s functions for powers of the invariant Laplacian and to the Minakshisundaram-Pleijel zeta function.

An accurate approximation of zeta-generalized-Euler-constant functions

Vito Lampret (2010)

Open Mathematics

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Zeta-generalized-Euler-constant functions, γ s : = ∑ k = 1 ∞ 1 k s - ∫ k k + 1 d x x s and γ ˜ s : = ∑ k = 1 ∞ - 1 k + 1 1 k s - ∫ k k + 1 d x x s defined on the closed interval [0, ∞), where γ(1) is the Euler-Mascheroni constant and γ ˜ (1) = ln 4 π , are studied and estimated with high accuracy.

Global existence for a nuclear fluid in one dimension: the T > 0 case

Bernard Ducomet (2002)

Applications of Mathematics

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We consider a simplified one-dimensional thermal model of nuclear matter, described by a system of Navier-Stokes-Poisson type, with a non monotone equation of state due to an effective nuclear interaction. We prove the existence of globally defined (large) solutions of the corresponding free boundary problem, with an exterior pressure P which is not required to be positive, provided sufficient thermal dissipation is present. We give also a partial description of the asymptotic behaviour...