An expansion formula for Fox's H-function

1969 ◽  
Vol 65 (3) ◽  
pp. 683-685 ◽  
Author(s):  
S. D. Bajpai
Keyword(s):  
Bessel Functions ◽  
Expansion Formula ◽  
Fox’S H Function

The object of this paper is to establish an integral involving Fox's H-function and employ it to obtain an expansion formula for the H-function involving Bessel functions.

SERIES EXPANSIONS OF THE GENERALIZED K-BESSEL FUNCTIONS ON SYMMETRIC CONES

2008 ◽  
Vol 06 (01) ◽  
pp. 1-10 ◽  
Author(s):  
HONGMING DING ◽  
WEI HE
Keyword(s):  
Series Expansion ◽  
Bessel Functions ◽  
Series Expansions ◽  
Symmetric Cones ◽  
Expansion Formula

In this paper, we generalize the series expansion formula of classical K-Bessel functions to symmetric cones.

An integral involving Fox's H-function and Whittaker functions

1969 ◽  
Vol 65 (3) ◽  
pp. 709-712 ◽  
Author(s):  
S. D. Bajpai
Keyword(s):  
Laguerre Polynomials ◽  
Whittaker Functions ◽  
Expansion Formula ◽  
Fox’S H Function

1. In this paper we have evaluated an integral involving Fox's H-functions and Whittaker functions. One particular case of the integral has been employed to establish an expansion formula for the H-function involving Laguerre polynomials.

scholarly journals Some expansion formulas for incomplete H- and H̅-functions involving Bessel functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sapna Meena ◽  
Sanjay Bhatter ◽  
Kamlesh Jangid ◽  
Sunil Dutt Purohit
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
Expansion Formula

Abstract In this paper, we assess an integral containing incomplete H-functions and utilize it to build up an expansion formula for the incomplete H-functions including the Bessel function. Next, we evaluate an integral containing incomplete H̅-functions and use it to develop an expansion formula for the incomplete H̅-functions including the Bessel function. The outcomes introduced in this paper are general in nature, and several particular cases can be acquired by giving specific values to the parameters engaged with the principle results. As particular cases, we derive expansions for the incomplete Meijer ${}^{(\Gamma )}G$ G ( Γ ) -function, Fox–Wright ${}_{p}\Psi _{q}^{(\Gamma )}$ Ψ q ( Γ ) p -function, and generalized hypergeometric ${}_{p}\Gamma _{q}$ Γ q p function.

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.

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