FIVE SERIES EQUATIONS INVOLVING GENERALIZED BATEMAN k-FUNCTIONS 


By

Omkar Lal Shrivastava¹∗ , Kuldeep Narain² and Sumita Shrivastava³

Department of Mathematics 

¹Government Kamladevi Rathi Girls Postgraduate College, Rajnandgaon, Chhattisgarh, India-491441 

²Kymore Science College, Kymore, Madhya Pradesh, India-483880 

³Government Digvijay Postgraduate College, Rajnandgaon, Chhattisgarh, India-491441 

Email: omkarlal@gmail.com, kuldeepnarain2009@gmail.com, sumitashrivastava9@gmail.com *Corresponding author email: omkarlal@gmail.com 

(Received: November 06, 2023; In format: November 13, 2023; Revised: January 10, 2024; Accepted: May 22, 2024) 


DOI: https://doi.org/10.58250/jnanabha.2024.54135 



Abstract

In this paper, the solution of five series equations involving generalized Bateman k-functions is obtained by reducing them to Fredholm integral equation of the second kind. The solution presented in this paper is obtained by employing the techniques of Narain and Lal [11] involving generalized Bateman k-functions by reducing them to the solution of a Fredholm inregral equation of second kind with different bounday conditions. Thus we have seen that Bateman k-functions are having interesting properties to solve double, triple, quadruple and five series equations as special functions. These solutions are very useful in Mathematical and Quantum Physics, Aero and Fluid Dynamics and Thermodynamics. 


2020 Mathematical Sciences Classification: 45XX, 45B05, 45F10,33C45. 

Keywords and Phrases: Five Series equations, generalized Bateman k-functions, Fredholm integral equation. 

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