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Contractions of rotation groups and their representations

Published online by Cambridge University Press:  24 October 2008

A. H. Dooley  and
J. W. Rice
A. H. Dooley
Affiliation:
School of Mathematics, University of New South Wales
J. W. Rice
Affiliation:
School of Mathematical Sciences, Flinders University
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Extract

It is a classical result in the theory of special functions that Bessel functions are limits in an appropriate sense of Legendre polynomials. For example in (11), § 17.4, the following result is attributed to Heine:

such limiting formulae are also known for certain other special functions (cf. (1), (5)). Apart from their intrinsic interest, these formulae have been used in the theory of special functions to obtain product formulae, etc. for the limit function from those of the approximating sequence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 509 - 517
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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