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Big q-Legendre polynomials

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In mathematics, the big q-Legendre polynomials are an orthogonal family of polynomials defined in terms of Heine's basic hypergeometric series as[1]

.

They obey the orthogonality relation

and have the limiting behavior

where is the th Legendre polynomial.[citation needed]

References

[edit]
  1. ^ Roelof Koekoek, Peter Lesky, Rene Swattouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, p 443, Springer