Eulerian numbers with fractional order parameters

DOI10.1007/BF01834003zbMath0797.11025OpenAlexW2053011928WikidataQ56852790 ScholiaQ56852790MaRDI QIDQ1312264

M. Hauss, Paul L. Butzer

Publication date: 6 February 1994

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137545

zbMATH Keywords

generating functionhypergeometric functionrecursion formulaeEulerian numbersEulerian functionsfractional Stirling numbers of second kindfractional Weyl integralWorpitzky formula

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Bernoulli and Euler numbers and polynomials (11B68) Fractional derivatives and integrals (26A33) Recurrences (11B37) Special sequences and polynomials (11B83) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items

A \(q\)-analog of Newton's series, Stirling functions and Eulerian functions, Double interpolation of the Euler numbers, On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations, Eulerian fractions and Stirling, Bernoulli and Euler functions with complex order parameters and their impact on the polylogarithm function, Some applications of the generalized Eulerian numbers, Unnamed Item, Bernoulli numbers and polynomials of arbitrary complex indices, Some new identities and inequalities for Bernoulli polynomials and numbers of higher order related to the Stirling and Catalan numbers, Euler–Frobenius numbers, Fractional calculus in the Mellin setting and Hadamard-type fractional integrals

Cites Work

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• Stirling polynomials
• Extended Bernoulli and Eulerian numbers
• Eine neue Einteilung der Permutationen
• Eulerian Numbers and Polynomials
• On Stirling Functions of the Second Kind
• An Approach to Fractional Powers of Operators via Fractional Differences
• Über Stirlingsche Zahlen 2. Art.
• Asymptotic properties of eulerian numbers
• Iterated Sums of Powers of the Binomial Coefficients
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