Tangent numbers and operators

DOI10.1215/S0012-7094-72-03949-XzbMath0243.05009OpenAlexW2084257191MaRDI QIDQ2554330

Leonard Carlitz, Richard Scoville

Publication date: 1972

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-72-03949-x

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (19)

Unnamed Item ⋮ A class of Frobenius-type Eulerian polynomials ⋮ The Dumont ansatz for the Eulerian polynomials, peak polynomials and derivative polynomials ⋮ A grammatical calculus for peaks and runs of permutations ⋮ An explicit formula for the number of permutations with a given number of alternating runs ⋮ The free tangent law ⋮ Derivative polynomials and enumeration of permutations by number of interior and left peaks ⋮ Higher-order tangent and secant numbers ⋮ Central factorial numbers; their main properties and some applications. ⋮ The Lerch zeta and related functions of non-positive integer order ⋮ Closed formulas for computing higher-order derivatives of functions involving exponential functions ⋮ The trace method for cotangent sums ⋮ Fermi-Dirac and Bose-Einstein functions of negative integer order ⋮ The umbral calculus ⋮ The \(r\)-alternating permutations ⋮ Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals ⋮ Alternating Eulerian polynomials and left peak polynomials ⋮ Derivative polynomials and closed-form higher derivative formulae ⋮ Chapter 7 of Ramanujan's second notebook

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