z]; Rosenbloom , who discussed the angular distribution of zeros using potential theory, and applied his work to the sub-class of confluent hypergeometric functions
; Erdos and Turan , who used minimization techniques to discuss angular distributions of zeros; Newman and Rivlin [7, 8], who related the work of Szego to the Central Limit Theorem; Edrei, Saff and Varga , who gave a thorough analysis for the family of Mittag-Leffler functions; Carpenter, Varga and Waldvogel , who refined the work of Szego; Norfolk [9, 10], who refined the work of Rosenbloom on the confluent hypergeometric functions
and a related set of integral transforms.
This gives an expansion analogous to the Poincare-type expansion, but including confluent hypergeometric functions instead of inverse powers of z as asymptotic sequence.
The purpose of this paper is to analyze some features of this modification, namely the convergence properties of the modified asymptotic series and some techniques that can be used to compute the confluent hypergeometric functions involved in the approximation.
These integrals can be written as confluent hypergeometric functions, by virtue of the integral representation[1, Eq.
8), the modified asymptotic series involves confluent hypergeometric functions as the asymptotic sequence.
0] = 1, so it is important to observe that in this setting there is no need for the actual computation of the confluent hypergeometric functions.
These techniques can be applied to several other examples within the family of confluent hypergeometric functions.
SLATER, Confluent Hypergeometric Functions, Cambridge University Press, New York, 1960.
in terms of the confluent hypergeometric function of the first kind or Kummer function.