1303.0806 (Yoon Seok Choun)

Generalization of the three-term recurrence formula and its applications    [PDF]

Yoon Seok Choun

We generalize three term recurrence formula in linear differential equation. It is well known that all known special functions have only two term recursion relations. Linear differential equations has very long history over 500 years. During this period, mathematicians developed analytic solutions of only two term recursion relations. They do not know how to solve the case of three term recurrence formula. From our paper, we can get exact solution of the three term one, and we can express it by integral formalism and generating function of it. Furthermore, we will show, on the next paper, for the first time how to solve mathematical equations having three term recursion relations and go on producing the exact solutions of some of the well known special function theories that include Mathieu function, Heun's equation, Grand Confluent Hypergeometric(G.C.H.) Function, Lame Function. We hope these new functions and their solutions will produce remarkable new range of applications not only in supersymmetric field theories as is shown here, but in the areas of all different classes of mathematical physics, applied mathematics and in engineering applications.

View original: http://arxiv.org/abs/1303.0806