ON THE HUMBERT CONFLUENT HYPERGEOMETRIC FUNCTION

USED IN LASER FIELD

 

E.M. El Halba1, H. Nebdi1, M. Boustimi2, A. Belafhal1*

1Laboratory of Nuclear, Atomic and Molecular Physics
Department of Physics, Faculty of Sciences, Chouaïb Doukkali University,

P. B 20, 24000 El Jadida, Morocco

2Physics Department, College of Applied Sciences, Umm Al-Qura University,

P.O. Box : 715 , Makkah 21955, Saudi Arabia.

* Corresponding author: belafhal@gmail.com

Received: 06 December 2013; revised version accepted: 13 May 2014

 

Abstract

     Based upon the closed form of the Humbert confluent hypergeometric function Psi1, the properties of Gauss hypergeometric function F21 and the Pochhammer’s symbol, we investigate some transformation and representation formulas associated with Psi1 . Several equations are deduced in the present study. These results can be used in many physical areas, particularly in the description of the donut laser beams.

 

Keywords: Humbert confluent hypergeometric function; Gauss hypergeometric function; Pochhammer's symbol; Euler gamma function; Donut beams.

 


 

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