On some formulas for the K-analogue of appell functions and generating relations via K-fractional derivative
Abstract
Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol Diaz et al. 2017, which are one of the vital generalizations of hypergeometric functions. We introduce k-analogues of F2 and F3 Appell functions denoted by the symbols F2,k and F3,k, respectively, just like Mubeen et al. did for F1 in 2015. Meanwhile, we prove integral representations of the k-generalizations of F2 and F3 which provide us with an opportunity to generalize widely used identities for Appell hypergeometric functions. In addition, 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. Finally, 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. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
Source
Fractal and FractionalVolume
4Issue
4Collections
Related items
Showing items related by title, author, creator and subject.
-
Effect of epicardial adipose tissue on diastolic functions and left atrial dimension in untreated hypertensive patients with normal systolic function
Çetin, Mustafa; Kocaman, Sinan Altan; Durakoğlugil, Murtaza Emre; Erdoğan, Turan; Ergül, Elif; Doğan, Sıtkı; Canga, Aytun (Elsevier, 2013)Background: Adipose tissue is the source of many adipokines affecting the cardiovascular system either locally or systemically. Although hypertension is one of the most important factors in diastolic dysfunction (DD), the ... -
The relationship between ascending aortic diameter with left atrial functions and left ventricular mass index in a population with normal left ventricular systolic function
Ergül, Elif; Özyıldız, Ali Gökhan; Emlek, Nadir; Özyıldız, Afag; Durak, Hüseyin; Duman, Hakan (Wiley, 2023)AimAscending aortic dilatation is a common clinical issue. In the present study, we aimed to evaluate the relationship between ascending aortic diameter with left ventricular (LV) and left atrial (LA) functions, and LV ... -
Serum osteoprotegerin level is independently related to subclinical left atrial mechanical function in patients with hypertension and diabetes
Kalaycıoğlu, Ezgi; Çetin, Mustafa; Çinier, Göksel; Kırış, Tuncay; Gökdeniz, Tayyar; Özyıldız, Ali Gökhan; Durmus, Ismet (Urban & Vogel, 2020)Objectives Previous studies showed that subclinical abnormal left atrial (LA) function could be diagnosed with LA speckle tracking evaluation long before chamber enlargement. Osteoprotegerin (OPG) is a member of the tumor ...