scholarly journals On Decomposition Formulas Related to the Gaussian Hypergeometric Functions in Three Variables

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Anvar Hasanov ◽  
Jihad Younis ◽  
Hassen Aydi
Keyword(s):  
Hypergeometric Functions ◽  
Gaussian Hypergeometric Functions ◽  
Transformation Formulas

In this paper, by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011, we establish several decomposition formulas associated with the Gaussian triple hypergeometric functions. Some transformation formulas for these functions have also been obtained.

scholarly journals On transformation formulas for theta hypergeometric functions

2012 ◽  
Vol 64 (7) ◽  
pp. 1136-1143
Author(s):  
R. Y. Denis ◽  
S. N. Singh ◽  
S. P. Singh
Keyword(s):  
Hypergeometric Functions ◽  
Transformation Formulas

scholarly journals Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions

2018 ◽  
Vol 3 (2) ◽  
pp. 331-338 ◽  
Author(s):  
Ahmed Ali Atash ◽  
Hussein Saleh Bellehaj
Keyword(s):  
Generating Functions ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
General Transformation ◽  
Summation Theorem ◽  
Transformation Formulas

AbstractIn this paper, we establish two general transformation formulas for Exton’s quadruple hypergeometric functions K5 and K12 by application of the generalized Kummer’s summation theorem. Further, a number of generating functions for Jacobi polynomials are also derived as an applications of our main results.

scholarly journals Some Transformation Formulas for Lauricella's Hypergeometric Functions FD

2009 ◽  
Vol 52 (2) ◽  
pp. 203-212 ◽  
Author(s):  
Keiji Matsumoto ◽  
Katsuyoshi Ohara
Keyword(s):  
Hypergeometric Functions ◽  
Transformation Formulas

scholarly journals Some Incomplete Hypergeometric Functions and Incomplete Riemann-Liouville Fractional Integral Operators

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 483 ◽  
Author(s):  
Mehmet Ali Özarslan ◽  
Ceren Ustaoğlu
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Integral ◽  
Recurrence Relations ◽  
Beta Function ◽  
Integral Operators ◽  
Integral Representations ◽  
Fractional Integral Operators ◽  
Derivative Formulas ◽  
Generating Relations ◽  
Transformation Formulas

Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function B y ( x , z ) . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relations. Furthermore, incomplete Riemann-Liouville fractional integral operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions.

scholarly journals On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

2020 ◽  
Vol 4 (4) ◽  
pp. 48 ◽  
Author(s):  
Övgü Gürel Yılmaz ◽  
Rabia Aktaş ◽  
Fatma Taşdelen
Keyword(s):  
Fractional Derivative ◽  
Hypergeometric Functions ◽  
Close Relation ◽  
Generating Relations ◽  
Transformation Formulas ◽  
Appell Functions

Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol in Diaz et al. 2007, which are one of the vital generalizations of hypergeometric functions. In this study, we focus on the k-analogues of F1Appell function introduced by Mubeen et al. 2015 and the k-generalizations of F2 and F3 Appell functions indicated in Kıymaz et al. 2017. we present some important transformation formulas and some reduction formulas which show close relation not only with k-Appell functions but also with k-hypergeometric functions. Employing the theory of Riemann–Liouville k-fractional derivative from Rahman et al. 2020, and using the relations which we consider in this paper, we acquire linear and bilinear generating relations for k-analogue of hypergeometric functions and Appell functions.

scholarly journals Landen Inequalities for Zero-Balanced Hypergeometric Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Slavko Simić ◽  
Matti Vuorinen
Keyword(s):  
Open Problem ◽  
Hypergeometric Functions ◽  
Elliptic Integral ◽  
Complete Elliptic Integral ◽  
Turn On ◽  
Gaussian Hypergeometric Functions

For zero-balanced Gaussian hypergeometric functionsF(a,b;a+b;x),a,b>0, we determine maximal regions ofabplane where well-known Landen identities for the complete elliptic integral of the first kind turn on respective inequalities valid for eachx∈(0,1). Thereby an exhausting answer is given to the open problem from the work by Anderson et al., 1990.

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