Continued fractions and \(q\)-series generating functions for the generalized sum-of-divisors functions

DOI10.1016/j.jnt.2017.05.023zbMath1421.11055arXiv1704.05200OpenAlexW2609338277MaRDI QIDQ2401215

Maxie D. Schmidt

Publication date: 31 August 2017

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.05200

zbMATH Keywords

divisor functioncontinued fractionsum of divisors functionJ-fraction

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Convergence and divergence of series and sequences of functions (40A30) Continued fractions and generalizations (11J70) Arithmetic functions; related numbers; inversion formulas (11A25) Continued fraction calculations (number-theoretic aspects) (11Y65)

Uses Software

• DLMF

Cites Work

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• New convolutions for the number of divisors
• Combinatorial interpretations of a recent convolution for the number of divisors of a positive integer
• On congruences and continued fractions for some classical combinatorial quantities
• Non-central generalized \(q\)-factorial coefficients and \(q\)-Stirling numbers
• Some \(q\)-series identities related to divisor functions
• A new look on the generating function for the number of divisors
• A connection between Jacobi-Stirling numbers and Bernoulli polynomials
• A generating function for \(\sigma(3n-1)\)
• Combinatorial aspects of continued fractions. (Reprint)
• Commutation Relations, Normal Ordering, and Stirling Numbers

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