Definition
In general, the orthogonal polynomials Pn with respect to a weight W:R→R+ on the real line are defined by
The relations above define Pn up to multiplication by a number. Various normalisations are used to fix the constant, e.g.
The classical orthogonal polynomials correspond to the three families of weights:
The standard normalisation (also called standardization) is detailed below.
Read more about this topic: Classical Orthogonal Polynomials
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