International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 545-550

Fibonacci polynominals of order k, multinomial expansions and probability

Andreas N. Philippou,1 Costas Georghiou,2 and George N. Philippou3

1Department of Mathematics, Univeristy of Patras, Patras, Greece
2School of Engineering, Univeristy of Patras, Patras, Greece
3Department of General Studies, Higher Technical Institute, Nicosia, Cyprus

Received 31 October 1982

Copyright © 1983 Andreas N. Philippou et al. 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 Fibonacci polynomials of order k are introduced and two expansions of them are obtained, in terms of the multinomial and binomial coefficients, respectively. A relation between them and probability is also established. The present work generalizes results of [2] - [4] and [5].