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The product of two ultraspherical polynomials

Published online by Cambridge University Press:  18 May 2009

L. Carlitz
L. Carlitz
Affiliation:
Duke University, Durham, North Carolina
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Let

It is familiar that

(1) In the addition theorem [3, p. 363]

where

take θ = π and replace v by v−½. Since

we get

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 2 , July 1961 , pp. 76 - 79
Copyright
Copyright © Glasgow Mathematical Journal Trust 1961

References

Al-Salam, W. A., On the product of two Legendre polynomials, Math. Scand. 4 (1956), 239–242.CrossRefGoogle Scholar
Bailey, W. N., On the product of two associated Legendre functions, Quart. J. Math. Oxford Ser. (2) 11 (1940), 30–35.Google Scholar
Watson, G. N., Theory of Bessel functions (second edn, Cambridge 1944).Google Scholar
Whittaker, E. T. and Watson, G. N., A course of modern analysis (fourth edn, Cambridge, 1927)Google Scholar