Jacobi Type Continued Fractions for the Ordinary Generating Functions of Generalized Factorial Functions

zbMath1355.05012arXiv1610.09691MaRDI QIDQ2963480

Maxie D. Schmidt

Publication date: 14 February 2017

Full work available at URL: https://arxiv.org/abs/1610.09691

zbMATH Keywords

Hadamard productLaguerre polynomialconfluent hypergeometric functioncontinued fractionfactorial functionPochhammer symbolgeneralized Stirling numberStirling number of the first kindrising factorialPochhammer \(k\)-symbolordinary generating functionBarnes \(G\)-functionS-fractiondouble factorialJ-fractionsuperfactorialdiagonal generating functiondivergent ordinary generating functionformal Laplace-Borel transformhyperfactorialmultifactorialmultiple factorialStirling number congruencesubfactorialtriple factorial

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Continued fractions (11A55) Continued fraction calculations (number-theoretic aspects) (11Y65) Calculation of integer sequences (11Y55)

Related Items (4)

Continued fractions for square series generating functions ⋮ Jacobi-Type Continued Fractions and Congruences for Binomial Coefficients Modulo Integers $h \geq 2$ ⋮ New Congruences and Finite Difference Equations for Generalized Factorial Functions ⋮ Combinatorial Identities for Generalized Stirling Numbers Expanding $f$-Factorial Functions and the $f$-Harmonic Numbers

Uses Software

• DLMF
• OEIS
• Wolfram Functions Site

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