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 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 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 Certain transformations for hypergeometric series in the p-adic setting

2015 ◽  
Vol 11 (02) ◽  
pp. 645-660 ◽  
Author(s):  
Rupam Barman ◽  
Neelam Saikia
Keyword(s):  
Elliptic Curves ◽  
Finite Fields ◽  
Gamma Function ◽  
Hypergeometric Functions ◽  
Hypergeometric Series ◽  
Transformation Formulas ◽  
Trace Of Frobenius

In [The trace of Frobenius of elliptic curves and the p-adic gamma function, Pacific J. Math. 261(1) (2013) 219–236], McCarthy defined a function nGn[⋯] using the Teichmüller character of finite fields and quotients of the p-adic gamma function. This function extends hypergeometric functions over finite fields to the p-adic setting. In this paper, we give certain transformation formulas for the function nGn[⋯] which are not implied from the analogous hypergeometric functions over finite fields.

q-Integral and Moment Representations for q-Orthogonal Polynomials

2002 ◽  
Vol 54 (4) ◽  
pp. 709-735 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
Dennis Stanton
Keyword(s):  
Orthogonal Polynomials ◽  
Exponential Function ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Integral Representations ◽  
Basic Hypergeometric Functions ◽  
Transformation Formulas

AbstractWe develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.

scholarly journals Transformation formulas of incomplete hypergeometric functions via fractional calculus operators

2021 ◽  
Vol 13(62) (2) ◽  
pp. 571-580
Author(s):  
Kamlesh Jangid ◽  
Sunil Dutt Purohit ◽  
Daya Lal Suthar
Keyword(s):  
Fractional Calculus ◽  
Hypergeometric Function ◽  
Present Article ◽  
Hypergeometric Functions ◽  
Fractional Calculus Operators ◽  
Transformation Formulas

The desire for present article is to derive from the application of fractional calculus operators a transformation that expresses a potentially useful incomplete hypergeometric function in various forms of a countable sum of lesser-order functions. Often listed are numerous (known or new) specific cases and implications of the findings described herein

scholarly journals Extended incomplete version of hypergeometric functions

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 653-662
Author(s):  
Mehmet Özarslan ◽  
Ceren Ustaoğlu
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Derivatives ◽  
Integral Representations ◽  
Elementary Functions ◽  
Gamma Functions ◽  
Mellin Transforms ◽  
Incomplete Gamma Functions ◽  
Derivative Formulas ◽  
Transformation Formulas

Recently, the incomplete Pochhammer ratios are defined in terms of incomplete beta and gamma functions [10]. In this paper, we introduce the extended incomplete version of Pochhammer symbols in terms of the generalized incomplete gamma functions. With the help of this extended incomplete version of Pochhammer symbols we introduce the extended incomplete version of Gauss hypergeometric and Appell?s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, Mellin transforms and log convex properties. Furthermore, we investigate incomplete fractional derivatives for extended incomplete version of some elementary functions.

Some Properties of Extended Hypergeometric Function and Its Transformations

2018 ◽  
Vol 85 (3-4) ◽  
pp. 305
Author(s):  
Aparna Chaturvedi ◽  
Prakriti Rai
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Beta Function ◽  
Gauss Hypergeometric Function ◽  
Confluent Hypergeometric Functions ◽  
Mellin Transformation ◽  
Transformation Formulas

There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.

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