%0 Journal Article
%T Discrete Bernoulli's formula and its applications arising from generalized difference operator
%A G. Britto Antony Xavier
%A H. Nasira Begum
%J International Journal of Mathematical Analysis
%D 2013
%I 
%X In this paper, the authors derive discrete Bernoulli's formula of the form, [Delta_ell^{-1}[u(k) v(k)] = sumlimits_{t=0}^infty (-1)^t u^{(t)}(k) v_{t+1}(k+tell)]for the real valued real variable functions $u(k)$ and $v(k)$ using the generalized differences, $u^{(t)}(k)=Delta_ell^t u(k)$ and its inverses, $v_{t}(k)=Delta_ell^{-t} v(k)$ and obtain several formulae on finite and infinite series as application of the discrete Bernoulli's formula in number theory. Suitable examples are provided to illustrate the main results.
%K Generalized difference operator
%K Discrete Bernoulli¡¯s Formula
%K Partial sums
%U http://www.m-hikari.com/ijma/ijma-2013/ijma-5-8-2013/brittoIJMA5-8-2013.pdf