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Results tagged with orthogonal-polynomials
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user 49208
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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Legendre Q(n,x) function coefficients in terms of P(n,x) coefficients
The formular you search for is really known. It is on p. 360 of the NIST Handbook of Mathematical Functions, formulas (14.7.2)--(14.7.7). $p_n(x)$ is in fact an explicit polynomial (not rational) wit …
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