Combinatorial Identities for Generalized Stirling Numbers Expanding $f$-Factorial Functions and the $f$-Harmonic Numbers

zbMath1390.11051arXiv1611.04708MaRDI QIDQ4637132

Maxie D. Schmidt

Publication date: 18 April 2018

Full work available at URL: https://arxiv.org/abs/1611.04708

zbMATH Keywords

Stirling numberharmonic numberfactorialPochhammer symbolStirling polynomialmultifactorial\(j\)-factorial\(f\)-harmonic numbergen eralized Stirling number

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Factorials, binomial coefficients, combinatorial functions (05A10) Other combinatorial number theory (11B75)

Related Items (3)

An a priori harmonic mesh for singularly perturbed boundary value problems ⋮ Unnamed Item ⋮ Construction and computation of unified Stirling-type numbers emerging from \(p\)-adic integrals and symmetric polynomials

Uses Software

• DLMF

Cites Work

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• Divided differences and a general explicit formula for sequences of Mansour-Mulay-Shattuck
• A general two-term recurrence and its solution
• On Stirling numbers and Euler sums
• On the differences of the generalized factorials at an arbitrary point and their combinatorial applications
• Some asymptotic formulae for \(q\)-shifted factorials
• On the \(q\)-differences of the generalized \(q\)-factorials
• Jacobi Type Continued Fractions for the Ordinary Generating Functions of Generalized Factorial Functions
• Zeta Series Generating Function Transformations Related to Generalized Stirling Numbers and Partial Sums of the Hurwitz Zeta Function
• Generating Function Transformations Related to Polylogarithm Functions and the $k$-Order Harmonic Numbers

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