ARTICLE | doi:10.20944/preprints202011.0539.v2
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Fibonacci number; Lucas number; summation identity; series; digamma function; polygamma function; zeta function
Online: 3 February 2021 (10:29:55 CET)
We derive new infinite series involving Fibonacci numbers and Riemann zeta numbers. The calculations are facilitated by evaluating linear combinations of polygamma functions of the same order at certain arguments.
ARTICLE | doi:10.20944/preprints201703.0029.v1
Subject: Mathematics & Computer Science, Analysis Keywords: series identity; Catalan number; Catalan function; Riemanian zeta function; alternative Hurwitz zeta function; digamma function
Online: 6 March 2017 (07:01:20 CET)
In the paper, the authors discover several series identities involving the Catalan numbers, the Catalan function, the Riemanian zeta function, and the alternative Hurwitz zeta function.
ARTICLE | doi:10.20944/preprints202011.0463.v1
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Fibonacci number; Lucas number; summation identity; series; generating function; gamma function; digamma function; trigonometric functions; inverse tangent; bernoulli number; zeta function
Online: 18 November 2020 (10:19:50 CET)
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.