Functional inequalities for Gaussian hypergeometric function and generalized elliptic integral of the first kind

2021 ◽  
Vol 71 (3) ◽  
pp. 667-682
Author(s):  
Shen-Yang Tan ◽  
Ti-Ren Huang ◽  
Yu-Ming Chu
Keyword(s):  
Hypergeometric Function ◽  
Elliptic Integral ◽  
Functional Inequalities ◽  
Gaussian Hypergeometric Function

Abstract In the article, we present several new functional inequalities for the Gaussian hypergeometric function and generalized elliptic integral of the first kind.

scholarly journals Monotonicity, convexity properties and inequalities involving Gaussian hypergeometric functions with applications

2021 ◽  
Vol 7 (4) ◽  
pp. 4974-4991
Author(s):  
Ye-Cong Han ◽  
◽  
Chuan-Yu Cai ◽  
Ti-Ren Huang ◽  
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Elliptic Integral ◽  
Gaussian Hypergeometric Function ◽  
Gaussian Hypergeometric Functions ◽  
Convexity Properties

<abstract><p>In this paper, we mainly prove monotonicity and convexity properties of certain functions involving zero-balanced Gaussian hypergeometric function $ F(a, b; a+b; x) $. We generalize conclusions of elliptic integral to Gaussian hypergeometric function, and get some accurate inequalities about Gaussian hypergeometric function.</p></abstract>

scholarly journals MATHIEU-TYPE SERIES BUILT BY (p, q)-EXTENDED GAUSSIAN HYPERGEOMETRIC FUNCTION

2017 ◽  
Vol 54 (3) ◽  
pp. 789-797 ◽  
Author(s):  
Junesang Choi ◽  
Rakesh Kumar Parmar ◽  
Tibor K. Pogany
Keyword(s):  
Hypergeometric Function ◽  
Gaussian Hypergeometric Function ◽  
Type Series

A Class of Generalized Hypergeometric Functions in Several Variables

1992 ◽  
Vol 44 (6) ◽  
pp. 1317-1338 ◽  
Author(s):  
Zhimin Yan
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Hypergeometric Function ◽  
Unique Solution ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Gaussian Hypergeometric Function ◽  
Generalized Hypergeometric Functions ◽  
Several Variables

AbstractWe study a class of generalized hypergeometric functions in several variables introduced by A. Korânyi. It is shown that the generalized Gaussian hypergeometric function is the unique solution of a system partial differential equations. Analogues of some classical results such as Kummer relations and Euler integral representations are established. Asymptotic behavior of generalized hypergeometric functions is obtained which includes some known estimates.

scholarly journals Starlike and Convex Properties for Hypergeometric Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Oh Sang Kwon ◽  
Nak Eun Cho
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Gaussian Hypergeometric Function ◽  
Starlike And Convex Functions

The purpose of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.

DEVELOPMENT OF A GAUSSIAN HYPERGEOMETRIC FUNCTION CODE IN COMPLEX DOMAINS

1993 ◽  
Vol 04 (04) ◽  
pp. 805-840 ◽  
Author(s):  
YUPAI P. HSU
Keyword(s):  
Hypergeometric Function ◽  
Complex Plane ◽  
Gaussian Hypergeometric Function ◽  
Trigonometric Identity ◽  
Arbitrary Complex ◽  
Function Code

The analytic properties of the Gaussian hypergeometric function is reviewed and applied to the development of a Fortran function code. The code developed can be used to evaluate the hypergeometric function on the whole complex plane with arbitrary complex parametric values. In the process of numerically verifying the code, a trigonometric identity involving the hypergeometric function listed in most of the mathematical handbooks is found to be incorrectly stated.

scholarly journals A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order

2020 ◽  
Vol 13 (3) ◽  
pp. 587-607
Author(s):  
Nestor Gonzales Acala
Keyword(s):  
Hypergeometric Function ◽  
Explicit Formula ◽  
Higher Order ◽  
Gaussian Hypergeometric Function ◽  
Generalized Polynomials ◽  
New Class ◽  
Genocchi Polynomials

Most unifications of the classical or generalized Bernoulli, Euler, and Genocchi polynomials involve unifying any two or all of the three special types of polynomials (see, [1, 4, 9, 18, 19,21, 24–26, 30, 31]). In this paper, we introduce a new class of multiparameter Fubini-type gener-alized polynomials that unifies four families of higher order generalized Apostol-type polynomials such as the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Fubini polynomials. Moreover, we obtain an explicit formula of these unified generalized polynomials in terms of the Gaussian hypergeometric function, and establish several symmetry identities.

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