Hypergeometric Function and its Application on Heat Kernel in a Torus Surface with a Rectangular Lattice

Abstract

Hypergeometric functions are transcendental functions that are applicable in various branches of mathematics, physics, and engineering. They are solutions to a class of differential equations called hypergeometric differential equations. In this paper we will be using theta functions, null zeta function and Ramanujan’s identities to study the behavior of heat kernel in a torus surface with rectangular Lattice.