IJPAM: Volume 90, No. 2 (2014)

FINITE SERIES AND COMPLETE SOLUTION OF
SECOND ORDER $\alpha$-DIFFERENCE EQUATION

G. Britto Antony Xavier$^1$, P. Rajiniganth$^2$, V. Chandrasekar$^3$
$^1$ Department of Mathematics
Sacred Heart College
Tirupattur, 635601, Vellore District, Tamil Nadu, S. INDIA
$^2$ Department of Mathematics
SKP Institute of Technology
Tiruvannamalai, 606611, Tamil Nadu, S. INDIA
$^3$ Department of Mathematics
SKP Engineering College
Tiruvannamalai, 606611, Tamil Nadu, S. INDIA


Abstract. We derive the discrete version of Leibnitz Theorem, Montmorte's Theorem with respect to generalized $\alpha$-difference equation. We also investigate the numerical and complete solutions of second order $\alpha$-difference equation for finding the values of various finite $\alpha$-series in the field of finite difference method.

Received: September 18, 2013

AMS Subject Classification: 39A70, 47B39, 39A10

Key Words and Phrases: generalized $\alpha$-difference equation, numerical solution, complete solution, generalized polynomial factorial

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DOI: 10.12732/ijpam.v90i2.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 2