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Results tagged with orthogonal-polynomials
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user 40893
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 are many different families of orthogonal polynomials, among which one can cite Hermite polynomials, Laguerre polynomials, and Jacobi polynomials.
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What are the orthogonal polynomials with respect to the weight $2\cosh(\beta x)e^{-x^2}$?
In the study of a statistical physics problem, I need to know the orthogonal polynomials with respect to the weight
$$2\cosh(\beta x)e^{-x^2},$$
where $\beta \in \mathbb{R}^+$. Is this already known? …
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