scholarly journals Probabilistic proof of product formulas for Bessel functions

Bernoulli ◽  
2015 ◽  
Vol 21 (4) ◽  
pp. 2419-2429
Author(s):  
Luc Deleaval ◽  
Nizar Demni
Keyword(s):  
Bessel Functions ◽  
Probabilistic Proof ◽  
Product Formulas

An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions

1992 ◽  
Vol 44 (4) ◽  
pp. 867-879 ◽  
Author(s):  
René F. Swarttouw
Keyword(s):  
Integral Representation ◽  
Bessel Functions ◽  
Addition Theorem ◽  
Orthogonality Relation ◽  
Addition Formula ◽  
Ultraspherical Polynomials ◽  
Product Formulas

AbstractIn this paper a q-analogue of Gegenbauer's addition formula for Bessel functions is obtained by using the orthogonality relation for the q-Ultraspherical polynomials of Rogers'. Also some product formulas and an integral representation for the Hahn-Exton q-Bessel functions are obtained.

An Addition Theorem and Some Product Formulas for q-Bessel Functions

1988 ◽  
Vol 40 (5) ◽  
pp. 1203-1221 ◽  
Author(s):  
Mizan Rahman
Keyword(s):  
Bessel Function ◽  
Gamma Function ◽  
Bessel Functions ◽  
Series Representation ◽  
Addition Theorem ◽  
Image Position ◽  
Product Formulas

The most familiar series representation of the Bessel function is1.1Jackson [12] gave the following q-analogues:1.21.3where 0 < q < 1, the q-shifted factorials are defined by1.4and the q-gamma function is given by1.5

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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