Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: Youssef et al. as discussed by the authors considered a half-space filled with an elastic material, which has constant elastic parameters, and the governing equations are taken in the context of the two-temperature generalized thermoelasticity theory.
120 citations
TL;DR: In this article, an eigenvalue problem encountered in the dynamical theory of chain molecules is solved by three methods: use of a Fourier series for α, expansion of α in associated Legendre polynomials Pm2, and by a variation method.
Abstract: An eigenvalue problem encountered in the dynamical theory of chain molecules is ∫ −11α′′(s)(|r−s|)−12ds=−λα(r),α′(±1)=0. This is solved by three methods: use of a Fourier series for α, expansion of α in associated Legendre polynomials Pm2, and by a variation method. The eight smallest eigenvalues are calculated explicitly and an approximate formula is found for the remaining ones. Formulas are found also for the eigenfunctions.
120 citations
TL;DR: The approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic.
120 citations
119 citations
TL;DR: In this article, the authors considered the problem of a half-space formed of a material with variable thermal conductivity and applied the theory of fractional order theory of thermoelasticity to the problem.
119 citations