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A New Proof of a Watson's Formula

Published online by Cambridge University Press:  20 November 2018

Krzysztof Stempak
Krzysztof Stempak*
Affiliation:
Institute of Mathematics, University of WroclawPL. Grunwaldzki 2/4, 50-384 Wroclaw, Poland(Current Address) Department of Mathematics, The University of GeorgiaAthens, Georgia 30602, USA
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Abstract

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A new proof of a product formula for Laguerre polynomials, due originally to Watson, is given. Considering the commutative Banach algebra of radial functions on the Heisenberg groups Hn, n ≧ 2, we observe that Watson's formula holds for z = 1,2, 3, …. Then, applying a complex function theory argument, we establish the validity of this formula for other complex values of z, i.e. for Re z > - 1/2.

Keywords

Laguerre polynomialsHeisenberg groups33A6533A7543A80
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 414 - 418
Copyright
Copyright © Canadian Mathematical Society 1988

References

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