Extension of geometric series to hypergeometric function in Hindu mathematics

Abstract

The eastern society is rich in terms of science and technology. Mathematics is considered as the base of science. The eastern history shows that the Hindu society is rich in mathematics. The evolution of mathematics can be studied from the time of ‘patiganita’ to the latest form of science and technology. Geometric series is an important tool in arithmetic which is now developed to hypergeometric function. Hypergeometric function is an advance function used to solve differential equations of second order. The purpose of this paper is to find the linkage between the ancient geometric series (Gunanka sreni) to the modern Hypergeometric function and to expose the work of ancient Hindu mathematicians which is believed to be narrow among the mathematics researchers of the present period. In this paper, some forms of geometric series that were used in Hindu mathematics are interpreted in terms of hypergeometric series.