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The Generalized <i>r</i>-Whitney Numbers
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
- 3 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
Applied Mathematics·Volume 08 (2017)·Pages 117–132·Published 11 January 2017·DOI10.4236/am.2017.81010
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Abstract
In this paper, we define the generalized r -Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.
KeywordsWhitney Numbers<i>r</i>-Whitney Numbers<i>p</i>-Stirling NumbersGeneralized <i>q</i>-Stirling NumbersGeneralized Stirling Numbers
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