\(\alpha\)-Difference Operator and Its Application on Number Theory

  • Maria Susai Manuel RMD Engineering College
  • G.Britto Antony Xavier Sacred Heart College
  • Dilip D S Sacred Heart College


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.
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: 21 mar. 2018. doi: https://doi.org/10.20454/jmmnm.2012.435.