Fractional integral and other linear operators associated with the gaussian hypergeometric function

1997 ◽  
Vol 34 (3) ◽  
pp. 293-312 ◽  
Author(s):  
Yong Chan Kim ◽  
H. M. Srivastava
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Linear Operators ◽  
Gaussian Hypergeometric Function

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

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals On weighted inequalities for certain fractional integral operators

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
R. K. Raina
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Weighted Inequalities ◽  
Fractional Integral Operators

This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators. Multidimensional fractional integral operators involving the H-function are also introduced.

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.

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