Some Results on the Extended Hypergeometric Function
The Journal of the Indian Mathematical Society, 2020 An attempt is made to define the extended Pochhammer symbol (λ)n,α which leads to an extension of the classical hypergeometric functions. Differential equations and some properties have also been discussed.
Jana, Ranjan Kumar +2 more
openaire +1 more source
ON A NEW GENERALIZED BETA FUNCTION DEFINED BY THE GENERALIZED WRIGHT FUNCTION AND ITS APPLICATIONS
Malaysian Journal of Computing, 2021 Various extensions of classical gamma, beta, Gauss hypergeometric and confluent hypergeometric functions have been proposed recently by many researchers. In this paper, further generalized extended beta function with some of its properties like summation
Umar Muhammad Abubakar, Saroj Patel
doaj +1 more source
A New Class of Extended Hypergeometric Functions Related to Fractional Integration and Transforms
Journal of Mathematics, 2022 The focus of this research is to use a new extended beta function and develop the extensions of Gauss hypergeometric functions and confluent hypergeometric function formulas that are presumed to be new.
Vandana Palsaniya +3 more
doaj +1 more source
The c-function expansion of a basic hypergeometric function associated to root systems [PDF]
, 2014 We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by Cherednik in case ...
Gasper +11 more
core +4 more sources
Inequalities of extended beta and extended hypergeometric functions [PDF]
Journal of Inequalities and Applications, 2017 This paper studies the log-convexity of the extended beta functions. As a consequence, Tur n-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions,.
openaire +5 more sources
Extended elliptic-type integrals with associated properties and Turán-type inequalities
Advances in Difference Equations, 2021 Our aim is to study and investigate the family of ( p , q ) $(p, q)$ -extended (incomplete and complete) elliptic-type integrals for which the usual properties and representations of various known results of the (classical) elliptic integrals are ...
Rakesh K. Parmar +3 more
doaj +1 more source
Study of the Hypergeometric Equation via Data Driven Koopman-EDMD Theory
Axioms, 2023 We consider a data-driven method, which combines Koopman operator theory with Extended Dynamic Mode Decomposition. We apply this method to the hypergeometric equation which is the Fuchsian equation with three regular singular points.
Evangelos Melas +4 more
doaj +1 more source
Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x) [PDF]
, 2010 We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial ...
Miller, A. R., Paris, Richard B.
core +3 more sources
Extended incomplete version of hypergeometric functions
Filomat, 2020 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.
Özarslan, Mehmet Ali, Ustaoğlu, Ceren
openaire +2 more sources
EXTENSION OF EXTENDED BETA, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS
Honam Mathematical Journal, 2014 Summary: Recently several authors have extended the gamma function, beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions.
Choi, Junesang +2 more
openaire +2 more sources