$$\alpha$$-Difference Operator and Its Application on Number Theory

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Maria Susai Manuel G.Britto Antony Xavier Dilip D S

Abstract

In this paper, the authors define the generalized $$\alpha$$-difference operator $$\Delta_{\alpha(\ell)}$$ for positive real $\ell$ and obtain formulae on the sums of products of $$k^m$$, $$k_\ell^{(m)}$$ and powers of $$\alpha$$ using inverse operator $$\Delta_{\alpha(\ell)}^{-1}$$. Suitable examples are provided to illustrate the main results.

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How to Cite
MANUEL, Maria Susai; XAVIER, G.Britto Antony; D S, Dilip. $$\alpha$$-Difference Operator and Its Application on Number Theory. Journal of Modern Methods in Numerical Mathematics, [S.l.], v. 3, n. 2, p. 79-95, july 2012. ISSN 2090-4770. Available at: <http://www.m-sciences.com/index.php?journal=jmmnm&page=article&op=view&path%5B%5D=435>. Date accessed: 23 nov. 2017. doi: https://doi.org/10.20454/jmmnm.2012.435.
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