Hurwitz continued fractions with confluent hypergeometric functions

The Last of the Hypergeometric Continued Fractions *

A contiguous relation for complementry pairs of very well poised balanced 10φ9 basic hypergeometric functions is used to derive an explict expression for the associated continued fraction. This generalizes the continued fraction results associated with both Ramanujan’s Entry 40 and Askey-Wilson polynomials which can be recovered as limits. Associated with our continued fraction results there ar...

Continued Fractions of Tails of Hypergeometric Series

The tails of the Taylor series for many standard functions such as arctan and log can be expressed as continued fractions in a variety of ways. A surprising side effect is that some of these continued fractions provide a dramatic acceleration for the underlying power series. These investigations were motivated by a surprising observation about Gregory’s series. Gregory’s series for π, truncated...

Asymptotic Representations of Confluent Hypergeometric Functions.

I A more general theory will result if in the place of R we employ an abstract normed ring. s We use the symbols =, ... ... in more than one sense. No confusion need arise as tie context makes clear the meaning of each such symbol. It is worth while to mention here that the relation of equality = for E1 as well as for E2 is not an independent primitive idea; for, an equivalent set of postulates...

Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions

Moments of Hypergeometric Hurwitz Zeta Functions

This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called hypergeometric Hurwitz zeta functions, including their analytic continuation to the complex plane and a pre-functional equation satisfied by them. As an application, a formula for moments of hypergeometric H...