On the Solution of Simultaneous Triple Series Equations Involving Generalized Bateman-K Functions.

This paper presents a comprehensive analysis and solution methodology for simultaneous triple series equations involving generalized Bateman-k functions. The study extends the classical Bateman-k function, a notable special function in mathematical physics, to a more generalized form, enabling the exploration of its applications in solving complex simultaneous series equations. We derive explicit solutions by employing advanced mathematical techniques, including the method of integral transforms and series expansion. The results not only contribute to the theoretical understanding of Bateman-k functions but also offer practical computational tools for problems in mathematical physics, engineering, and applied mathematics where such functions naturally arise. The paper also discusses the convergence conditions and uniqueness of the solutions, providing a robust framework for future research in this area. In this paper an exact solution is obtained for the simultaneous triple series equations involving generalized Bateman k-Functions by multiplying factor method. [ABSTRACT FROM AUTHOR]