Extended Fibonacci numbers and polynomials with probability applications

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.

# Mathematics

Demetrios L. Antzoulakos (2004). "Extended Fibonacci numbers and polynomials with probability applications". International Journal of Mathematics and Mathematical Sciences. https://doi.org/10.1155/s016117120440458x