Contractions of rotation groups and their representations

Abstract

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.