Sum of Finite and Infinite Series Derived by Generalized Q-Alpha Derivative Operator

 International Journal of Mathematics Trends and Technology (IJMTT) © 2015 by IJMTT Journal Volume-24 Number-1 Year of Publication : 2015 Authors : G.Britto Antony Xavier, T.G.Gerly 10.14445/22315373/IJMTT-V24P509

G.Britto Antony Xavier, T.G.Gerly"Sum of Finite and Infinite Series Derived by Generalized Q-Alpha Derivative Operator", International Journal of Mathematics Trends and Technology (IJMTT). V24(1):67-72 August 2015. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In this paper, by defining the generalized q-derivative operator of first kind and its inverse, we obtain some identities and formulas on finite and infinite series in the field of finite difference methods. Suitable numerical examples verified by MATLAB are provided to illustrate the main results.

Reference
[1] Agarwal R.P., Difference Equations and Inequalities, Marcel Dekker, New York, 2000.
[2] Miller K.S., Ross B., Fractional difference calculus, in ”Univalent functions, fractional calculus and the applications(Koriyama, 1988)”, 139-152, Horwood, Chichester, 1989.
[3] Jackson F.H., On q-functions and a Certain Difference Operator, Trans. Roy.Soc.Edin, 46 (1908), 64-72.
[4] Jackson F.H., On q-definite integrals Qust.J. Pure Appl. Math. 41 (1910), 193-203.
[5] William Y.C.Chen and Gian-Carlo Rota, q-Analogs of the principle of Inclusion-Exclusion of restricted Position, Discrete Mathematics, 104 (1992), 7-22.
[6] William Y.C.Chen, Amy M.Fu and Baoyin Zhang, The Homogeneous q-Difference Operator, Advances in Applied Mathematics, 31 (2003), 659-668.
[7] Britto Antony Xavier G., Gerly T.G. and Nasira Begum H., Finite series of polynomials and polynomial factorials arising from generalised q_ difference operator, Far East Journal of Mathematical Sciences, 94(1) (2014), 47-63.
[8] Britto Antony Xavier G., Sathya S. and Vasantha Kumar S.U., n-Multi-Series of the Generalized Difference Equations to Circular Functions, International Journal of Mathematics Trends and Technology, 5 (2014), 97-107.
[9] Chandrasekar V. and Suresh K., Theory And Applications Of Generalized q-Derivative Operator, International Conference On Mathematical Computer Engineering - ICMCE - (2003), 703 - 709.
[10] Maria Susai Manuel M., Britto Antony Xavier G. and Thandapani E., Theory of Generalized Difference Operator and Its Applications, Far East Journal of Mathematical Sciences, 20(2) (2006), 163 - 171.

Keywords
Generalized q-alpha derivative operator, geometric progression and polynomial factorial.