Power sum identities with generalized Stirling numbers
Khristo N. Boyadzhiev
TL;DR
This paper presents new combinatorial identities involving generalized Stirling numbers, Stirling functions, binomial coefficients, and harmonic numbers, expanding the understanding of their interrelations.
Contribution
It introduces novel identities connecting Stirling functions of the second kind with complex variables to other combinatorial quantities.
Findings
New identities involving Stirling functions and numbers are established.
The identities connect Stirling functions with harmonic numbers and binomial coefficients.
Results extend classical combinatorial identities to complex variables.
Abstract
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical Inequalities and Applications · Functional Equations Stability Results