Bir Fibonacci ve Lucas dizisinde tekrarların bekleme süresi üzerine

Doğal fenomenlerin kesin bir manada tanımlanması, öngörülmesi ve anlaşılmasıyla ilgili yeni matematiksel aygıtlar geliştirmeihtiyacı giderek artmaktadır. Bu çalışmanın amacı, Fibonacci ve Lucas dizilerinin matematiksel çerçevesini modern matematikselformüller ile desteklemek amacıyla genişletmektir. Bu amaçla, order-k Fibonacci ve order-k Lucas dizileri ile eş zamanlı olarakBernoulli dizisine dayanarak analitik formüllerin türetilmesi amaçlanmaktadır. Ayrıca, k-yıncı mertebeden Fibonacci ve Lucas dizileriarasındaki bir ilişkiden yararlanarak (W (k)) bekleme süresinin olasılık dağılım fonksiyonu (pdf) çalışılacaktır.

On waiting time distribution of runs in a Fibonacci and Lucassequences

There is an increasingly needed to development a new mathematical apparatus concerned with the description, prediction, andunderstanding of natural phenomena in a precise manner. The purpose of this study is to extend the mathematical framework ofFibonacci and Lucas sequences for underpinned and establishing a modern mathematical formulas. For this purpose, we deriveanalytical formulas of order k-Fibonacci and order k-Lucas sequences simultaneously based on Bernoulli sequence. Furthermore,exploiting a relationship with the k th order Fibonacci and Lucas sequence, we study the probability distribution function (pdf) of thewaiting time (W (k)).

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