Quantum Algebra ε(2) and 2D q-Bessel Functions

2019 ◽  
Vol 83 (2) ◽  
pp. 191-206 ◽  
Author(s):  
Mumtaz Riyasat ◽  
Subuhi Khan ◽  
Tabinda Nahid
Keyword(s):  
Bessel Functions ◽  
Quantum Algebra

𝑞-Tricomi functions and quantum algebra representations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mumtaz Riyasat ◽  
Tabinda Nahid ◽  
Subuhi Khan
Keyword(s):  
Irreducible Representation ◽  
Series Expansion ◽  
Quantum Groups ◽  
Bessel Functions ◽  
Special Functions ◽  
Quantum Algebra ◽  
Two Dimensional ◽  
Quantum Algebras ◽  
Mathematical Software ◽  
First Time

AbstractThe quantum groups nowadays attract a considerable interest of mathematicians and physicists. The theory of 𝑞-special functions has received a group-theoretic interpretation using the techniques of quantum groups and quantum algebras. This paper focuses on introducing the 𝑞-Tricomi functions and 2D 𝑞-Tricomi functions through the generating function and series expansion and for the first time establishing a connecting relation between the 𝑞-Tricomi and 𝑞-Bessel functions. The behavior of these functions is described through shapes, and the contrast between them is observed using mathematical software. Further, the problem of framing the 𝑞-Tricomi and 2D 𝑞-Tricomi functions in the context of the irreducible representation (\omega) of the two-dimensional quantum algebra \mathcal{E}_{q}(2) is addressed, and certain relations involving these functions are obtained. 2-Variable 1-parameter 𝑞-Tricomi functions and their relationship with the 2-variable 1-parameter 𝑞-Bessel functions are also explored.

scholarly journals Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 198
Author(s):  
Yuriy Povstenko
Keyword(s):  
Heat Conduction ◽  
Fractional Calculus ◽  
Exponential Function ◽  
Nonlocal Elasticity ◽  
Bessel Functions ◽  
Wright Function ◽  
Mainardi Function ◽  
Integral Relations

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

scholarly journals A new product formula involving Bessel functions

2021 ◽  
pp. 1-17
Author(s):  
Mohamed Amine Boubatra ◽  
Selma Negzaoui ◽  
Mohamed Sifi
Keyword(s):  
Bessel Functions ◽  
New Product ◽  
Product Formula
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