Turán Type Inequalities for Tricomi Confluent Hypergeometric Functions

Turán type inequalities for q-hypergeometric functions

In this paper our aim is to deduce some Turán type inequalities for q-hypergeometric and q-confluent hypergeometric functions. In order to obtain the main results we apply the methods developed in the case of classical Kummer and Gauss hypergeometric functions. c ⃝ 2013 Elsevier Inc. All rights reserved.

Turán Type Inequalities for Hypergeometric Functions

In this note our aim is to establish a Turán type inequality for Gaussian hypergeometric functions. This result completes the earlier result that G. Gasper proved for Jacobi polynomials. Moreover, at the end of this note we present some open problems.

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

Polynomial series expansions for confluent and Gaussian hypergeometric functions

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions M(a, c; ·) and for Gaussian hypergeometric functions F (a, b; c; ·) are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions M(a, c; ·) and F (a, b; c; ·), in particular, if the parameters are al...