International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 134012 | https://doi.org/10.1155/S016117120440458X

Demetrios L. Antzoulakos, "Extended Fibonacci numbers and polynomials with probability applications", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 134012, 13 pages, 2004. https://doi.org/10.1155/S016117120440458X

Extended Fibonacci numbers and polynomials with probability applications

Received30 Apr 2004

Abstract

The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and polynomials are obtained. Interesting relations between them and probability problems which take into account lengths of success and failure runs are also established.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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