Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (4)

Search Parameters:
Keywords = k-Pochhammer symbol

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
12 pages, 261 KiB  
Article
On the Asymptotic Expansions of the (p,k)-Analogues of the Gamma Function and Associated Functions
by Tomislav Burić
Axioms 2025, 14(1), 55; https://doi.org/10.3390/axioms14010055 - 13 Jan 2025
Viewed by 701
Abstract
General asymptotic expansion of the (p,k)-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared. Results are applied to the analogues of digamma and [...] Read more.
General asymptotic expansion of the (p,k)-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared. Results are applied to the analogues of digamma and polygamma functions, and asymptotic expansion of the quotient of two (p,k)-gamma functions is also derived and analyzed. Various examples and application to the k-Pochhammer symbol are presented. Full article
(This article belongs to the Special Issue Special Functions and Related Topics)
15 pages, 287 KiB  
Article
Investigation of the k-Analogue of Gauss Hypergeometric Functions Constructed by the Hadamard Product
by Mohamed Abdalla and Muajebah Hidan
Symmetry 2021, 13(4), 714; https://doi.org/10.3390/sym13040714 - 18 Apr 2021
Cited by 5 | Viewed by 2655
Abstract
Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted [...] Read more.
Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted to the study of the k-analogue of Gauss hypergeometric functions by the Hadamard product. We give a definition of the Hadamard product of k-Gauss hypergeometric functions (HPkGHF) associated with the fourth numerator and two denominator parameters. In addition, convergence properties are derived from this function. We also discuss interesting properties such as derivative formulae, integral representations, and integral transforms including beta transform and Laplace transform. Furthermore, we investigate some contiguous function relations and differential equations connecting the HPkGHF. The current results are more general than previous ones. Moreover, the proposed results are useful in the theory of k-special functions where the hypergeometric function naturally occurs. Full article
(This article belongs to the Special Issue Special Functions and Polynomials)
20 pages, 347 KiB  
Article
On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative
by Övgü Gürel Yılmaz, Rabia Aktaş and Fatma Taşdelen
Fractal Fract. 2020, 4(4), 48; https://doi.org/10.3390/fractalfract4040048 - 24 Sep 2020
Cited by 12 | Viewed by 3233 | Correction
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fractional Calculus and Special Functions with Applications)
13 pages, 288 KiB  
Article
A New Representation of the k-Gamma Functions
by Asifa Tassaddiq
Mathematics 2019, 7(2), 133; https://doi.org/10.3390/math7020133 - 1 Feb 2019
Cited by 18 | Viewed by 6347
Abstract
The products of the form z ( z + l ) ( z + 2 l ) … ( z + ( k − 1 ) l ) are of interest for a wide-ranging audience. In particular, they frequently arise in diverse situations, [...] Read more.
The products of the form z ( z + l ) ( z + 2 l ) … ( z + ( k − 1 ) l ) are of interest for a wide-ranging audience. In particular, they frequently arise in diverse situations, such as computation of Feynman integrals, combinatory of creation, annihilation operators and in fractional calculus. These expressions can be successfully applied for stated applications by using a mathematical notion of k-gamma functions. In this paper, we develop a new series representation of k-gamma functions in terms of delta functions. It led to a novel extension of the applicability of k-gamma functions that introduced them as distributions defined for a specific set of functions. Full article
(This article belongs to the Special Issue Special Functions and Applications)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop