Series associated with a forgotten identity of N\"orlund
Kunle Adegoke, Robert Frontczak

TL;DR
This paper revisits Nörlund's series expression for the psi function to derive closed-form formulas for infinite series involving inverse factorials, Catalan numbers, and harmonic numbers, including new series for pi.
Contribution
It introduces new closed-form series involving inverse factorials, Catalan numbers, harmonic numbers, and pi, based on Nörlund's series expression for the psi function.
Findings
Derived closed-form expressions for series with inverse factorials.
Established new series involving Catalan numbers and harmonic numbers.
Proved novel series representations for pi.
Abstract
We apply a seemingly forgotten series expression of N\"orlund for the psi function to express infinite series involving inverse factorials in closed form. Many of such series contain products of Catalan numbers and (odd) harmonic numbers. We also prove some new series for .
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Taxonomy
TopicsHolomorphic and Operator Theory · Meromorphic and Entire Functions · Advanced Algebra and Geometry
