Tagged Questions

A familly of orthogonal polynomials is a sequence of polynomials in one variable, one in each degree, such that any two of them are orthogonal with respect to some fixed scalar product on the space of polynomials. They are closely related to continued fractions and useful in harmonic analysis. There ...

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Reasons for $\alpha>-\frac{1}{2}$ constraint in texts regarding Gegenbauer polynomials $C^{(\alpha)}_k(x)$

In texts regarding the Gegenbauer polynomials $C^{(\alpha)}_k(x)$, I often see the constraint $\alpha>-\frac{1}{2}$ alongside definitions and identities. I understand that the orthogonality ...
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What are the orthogonal polynomials w.r.t. Maxwell distribution

Is there a way to get a clean presentation of the orthogonal polynomials w.r.t. the Maxwell distribution https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution ? If you separate the ...
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Why decompose a function with eigenvectors of Laplace operator? [closed]

On periodic domain, people always use Fourier basis, which eigenvectors of Laplace operator. On sphere, people use spherical harmonics, which also are eigenvectors of Laplace operator. In applied ...
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