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Linearization of the Product of Jacobi Polynomials. II

Published online by Cambridge University Press:  20 November 2018

George Gasper
George Gasper*
Affiliation:
University of Toronto, Toronto, Ontario
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Let [3, p. 170, (16)]

(1.1)

denote the Jacobi polynomial of order (α, β), α, β > – 1, and let g(k, m, n; α, β) be denned by

(1.2)

where Rn(α, β)(x) = Pn(α, β)(x)/Pn(α, β)(1). It is well known [1; 2; 4; 5; 6] that the harmonic analysis of Jacobi polynomials depends, at crucial points, on the answers to the following two questions.

Question 1. For which (α, β) do we have

(1.3)

Question 2. For which (α, β) do we have

(1.4)

where G depends only on (α, β)?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 3 , 01 June 1970 , pp. 582 - 593
Copyright
Copyright © Canadian Mathematical Society 1970

References

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