Integral representations for multivariate logarithmic polynomials

DOI10.1016/j.cam.2017.11.047zbMath1400.11078OpenAlexW3123592378MaRDI QIDQ1696430

Feng Qi

Publication date: 14 February 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.20944/preprints201709.0112.v1

zbMATH Keywords

integral representationgenerating functioncompletely monotonic functionBernstein functionLévy-Khintchine representationmultivariate logarithmic polynomial

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Recurrences (11B37) Laplace transform (44A10) Special sequences and polynomials (11B83) Elementary classical functions (33B99) Monotonic functions, generalizations (26A48) Convergence and divergence of integrals (40A10)

Related Items (14)

The inverse of a triangular matrix and several identities of the Catalan numbers ⋮ Unnamed Item ⋮ Some inequalities and an application of exponential polynomials ⋮ Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ General Sets of Bell-Sheffer and Log-Sheffer Polynomials ⋮ Bell-Sheffer exponential polynomials of the second kind ⋮ On multivariate logarithmic polynomials and their properties ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ Logarithmic-Sheffer polynomials of the second kind ⋮ Unnamed Item ⋮ New Bell-Sheffer polynomial sets ⋮ Some identities for a sequence of unnamed polynomials connected with the Bell polynomials ⋮ Qi's conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and trigamma functions ⋮ Unnamed Item

Cites Work

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• Several closed expressions for the Euler numbers
• Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials
• A one-parameter family of Pick functions defined by the Gamma function and related to the volume of the unit ball in $n$-space
• SEVERAL FORMULAS FOR SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND AND APPLICATIONS
• AN INTEGRAL REPRESENTATION, SOME INEQUALITIES, AND COMPLETE MONOTONICITY OF THE BERNOULLI NUMBERS OF THE SECOND KIND
• Some properties of functions related to the gamma and psi functions
• Bernstein functions. Theory and applications

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