A New Class of Generalized on Generating Functions of Two Variables
- March 28, 2018
- Posted by: RSIS
- Category: Mathematics
International Journal of Research and Scientific Innovation (IJRSI) | Volume V, Issue III, March 2018 | ISSN 2321–2705
A New Class of Generalized on Generating Functions of Two Variables
L. K. Padhiary
Research Scholar, F. M. University. Balasore, (Odisha) India
Abstract: In this present paper a new class of generalized on generating functions of two variables has been introduced. We introduced generating functions of Polynomials of two variables and established a number of properties of the polynomials of two variables.
Key words: Generating function, Power series, Recurrence relation, Differential Recurrence relation.
I. INTRODUCTION
The Theory of generating function and recurrence relations play a very important role in the study of Discrite Mathematics and theory of special functions. Which has drawn in attention of several Mathematicians Scientists time to time.
According to Mc. Bride (1971). The term generating function is defined as follows
“ Let G(x, t) be a function that can be expended in the formal power series of ‘t’
such that
Where is a function of n, that may contain the paramaters of the polynomials
(x) but is independent of x and t. Then G(x,t) is called a generating function of the set (x) .
A generating functions plays on important role in defining a function and also mainly recurrence relations of differential types or pure types.
Rainvile (1967) developed a chapter to the generating function and differential recurrence relations of different types of polynomials. Srivastave and Manocha (1984) wrote a book on generating functions. In which they discussed the varities of generating functions and techniques including Lec algabric techniques. In the present chapter our objective is to introduce the generating fuction of two variables and to obtain differential recurrence relations.
If G(x,y,t) be a function. Which has a formal power series expansion in t as
