Submitted:
16 November 2020
Posted:
18 November 2020
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Abstract
We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.
Keywords:
Fibonacci number
; Lucas number
; summation identity
; series
; generating function
; gamma function
; digamma function
; trigonometric functions
; inverse tangent
; bernoulli number
; zeta function
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
