Fibonacci-Zeta infinite series associated with the polygamma functions
Kunle Adegoke, Sourangshu Ghosh
TL;DR
This paper introduces new infinite series combining Fibonacci numbers and Riemann zeta values, utilizing polygamma functions to facilitate the calculations, thus advancing the analytical tools for special series.
Contribution
It presents novel infinite series involving Fibonacci and zeta numbers derived through polygamma function evaluations, expanding the mathematical understanding of these special functions.
Findings
Derived new Fibonacci-zeta series using polygamma functions
Established connections between Fibonacci numbers and Riemann zeta values
Provided analytical formulas for complex series involving special functions
Abstract
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.
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