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Linearization of the Product of Jacobi Polynomials. I

Published online by Cambridge University Press:  20 November 2018

George Gasper
George Gasper*
Affiliation:
University of Toronto, Toronto, Ontario
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Let Pn(α,β) be the Jacobi polynomial of degree n, order (α,β), α,β > – 1, defined by

[9, p. 67], and let Rn(α,β)(x) = Pn(α,β)(x)/Pn(αβ)(1). Then for n ≧ m,

where

Since Rn(α, β)(l) = 1, it follows that

(1)

It is known that if (the ultraspherical case) or if α = β + 1, then α = β + 1, then g(k, n, m) ≧ 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 1 , 01 February 1970 , pp. 171 - 175
Copyright
Copyright © Canadian Mathematical Society 1970

References

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