International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 50, Pages 2681-2693
Extended Fibonacci numbers and polynomials with probability applications
Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou street, Piraeus 18534, Greece
Received 30 April 2004
Copyright © 2004 Demetrios L. Antzoulakos. 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.
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.