Abstract
AbstractThree 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.
Publisher
Cambridge University Press (CUP)
Cited by
6 articles.
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