Jñānābha‎, Vol. 49 (1) (2019), 89-96

A CLASS OF TWO VARIABLES SEQUENCE OF FUNCTIONS SATISFYING ABEL'S INTEGRAL EQUATION AND THE PHASE SHIFTS

Hemant Kumar

Department of Mathematics
D. A-V. Postgraduate College Kanpur - 208001, Uttar Pradesh, India
Email:palhemant2007@rediffmail.com
(Received : May 31, 2019 ; Revised: June 02, 2019)


Abstract

In this paper, we introduce a class of two variables sequence of functions as satisfying Abel's integral equation in which unknown function is the potential function and again consider that the Riemann - Liouville fractional integral of this class of functions equals to the slope of that potential function and then discuss some of its oscillatory properties and use them to evaluate the phase shifts in terms of arcsine of the series consisting of the Srivastava and Daoust's triple hypergeometric function.


2010 Mathematics Subject Classifications34 A08, 41A10, 34A45, 33C66, 33C90.
Keywords and phrasesA class of two variables sequence of functions, general sequences, phase shifts, Riemann - Liouville fractional integral, Kampé de Fériet function, Srivastava and Daoust function.