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Results tagged with orthogonal-polynomials
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user 87683
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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Are there graphs whose matching polynomials are Legendre?
It is well-known (at least well-known enough to be on Wikipedia) that there are quite simple graphs whose matching polynomials
$$M(G;x) = \sum_{m\geq 0} (-1)^m \#\{\text{matchings with $m$ edges}\}\ …
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