Neha Patil (Editor)

Continuous q Laguerre polynomials

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In mathematics, the continuous q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F. Swarttouw (2010, 14) give a detailed list of their properties.

Definition

The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by ]]。

P n ( α ) ( x | q ) = ( q α + 1 ; q ) n ( q ; q ) n 3 Φ 2 ( q n , q α / 2 + 1 / 4 e i θ , q α / 2 + 1 / 4 e i θ ; q α + 1 , 0 | q , q )

References

Continuous q-Laguerre polynomials Wikipedia