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Franz Neumann's integral of 1848

Published online by Cambridge University Press:  24 October 2008

E. R. Love
E. R. Love
Affiliation:
University of Melbourne
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Abstract

Three generalizations of Neumann's integral connecting the two kinds of Legendre function are obtained. They are not subject to restrictions that some parameter be integral, as the original formula and various known extensions of it all appear to be. These known extensions are exhibited as quite particular cases of the chief generalization obtained; and even when this generalization is specialized to the ‘unassociated’ Legendre functions of non-integral order it still seems to be new. Generalizations of Rodrigues's formula and of the orthogonality property are auxiliary results involved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 2 , April 1965 , pp. 445 - 456
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

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