# IJPAM: Volume 53, No. 1 (2009)

**ON GENERALIZED DIFFERENCE OPERATOR OF THIRD**

KIND AND ITS APPLICATIONS IN NUMBER THEORY

KIND AND ITS APPLICATIONS IN NUMBER THEORY

R. Pugalarasu, S. Elizabeth

Department of Mathematics

Sacred Heart College

Tirupattur, 635 601, Tamil Nadu, INDIA

e-mail: [email protected]

Department of Mathematics

Auxilium College

Vellore, Tamil Nadu, INDIA

**Abstract.**In this paper, the authors extend the theory of the generalized difference operator and the second kind
to the generalized difference operator of the third kind
for the positive reals and . We also present the discrete version of Leibnitz Theorem, binomial theorem, Newton's formula with reference to
Also by defining its inverse, we establish a few formulae for the sum of the second partial sums of higher powers of arithmetic progression in number theory.

**Received: **March 30, 2009

**AMS Subject Classification: **39A

**Key Words and Phrases: **generalized difference operator, generalized polynomial factorial, partial sums

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2009

**Volume:** 53

**Issue:** 1