This paper provides a proof, based on probabilistic arguments, of an asymptotic property of Kummer’s hypergeometric function M(a,b;z), valid when b and z are both large and approach +∞ and −∞, respectively, with the same order. The novelty of the result consists in the fact that, for its validity, no restriction is imposed on (the limiting value of) z/b, except that of being a negative number, whereas all the other known results require significant limitations.
A NOTE ON THE ASYMPTOTIC BEHAVIOR OF KUMMER’S HYPERGEOMETRIC FUNCTION WITH LARGE VALUES OF b AND z
Dolera, Emanuele
2019-01-01
Abstract
This paper provides a proof, based on probabilistic arguments, of an asymptotic property of Kummer’s hypergeometric function M(a,b;z), valid when b and z are both large and approach +∞ and −∞, respectively, with the same order. The novelty of the result consists in the fact that, for its validity, no restriction is imposed on (the limiting value of) z/b, except that of being a negative number, whereas all the other known results require significant limitations.File in questo prodotto:
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