Fibonacci - Home

If we compare Binet formulas (9) and (10) to the classical hyperbolic functions
wwe notice a similarity.
In [4], the discrete variable k in formulas (9) and (10) was replaced with the continuous variable x that takes its values from the
set of real numbers. Consequently, the following continuous functions, which are called the hyperbolic Fibonacci and the
Lucas functions, were introduced:
48
, (11)
. (12)
The hyperbolic Fibonacci sine
(13)
The hyperbolic Fibonacci cosine
(14)
The hyperbolic Lucas sine
(15)
The hyperbolic Lucas cosine