Article
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Fibonacci Series from Power Series
Version 1
: Received: 16 November 2020 / Approved: 18 November 2020 / Online: 18 November 2020 (10:19:50 CET)
How to cite: Adegoke, K. Fibonacci Series from Power Series. Preprints 2020, 2020110463. https://doi.org/10.20944/preprints202011.0463.v1 Adegoke, K. Fibonacci Series from Power Series. Preprints 2020, 2020110463. https://doi.org/10.20944/preprints202011.0463.v1
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
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: 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.
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