Remarks on Bell and higher order Bell polynomials and numbers

DOI10.1080/23311835.2016.1220670zbMath1430.11035OpenAlexW2514284557WikidataQ125667712 ScholiaQ125667712MaRDI QIDQ4966799

Paolo Emilio Ricci, Pierpaolo Natalini

Publication date: 27 June 2019

Published in: Cogent Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/23311835.2016.1220670

zbMATH Keywords

partitionsBell polynomialscombinatorial analysisdifferentiation of composite functionshigher-order Bell polynomials and numbersorthogonal polynomials and special functions

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81) Hypergeometric functions (33C99)

Related Items (12)

Finite-time ruin probabilities using bivariate Laguerre series ⋮ Higher order bell polynomials and the relevant integer sequences ⋮ Unnamed Item ⋮ Cumulative Parisian ruin in finite and infinite time horizons for a renewal risk process with exponential claims ⋮ 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 ⋮ Logarithmic-Sheffer polynomials of the second kind ⋮ Unnamed Item ⋮ New Bell-Sheffer polynomial sets ⋮ A new set of Sheffer-Bell polynomials and logarithmic numbers ⋮ Unnamed Item

Uses Software

• OEIS

Cites Work

• Repeated derivatives of composite functions and generalizations of the Leibniz rule
• New identities for the partial Bell polynomials
• Bell polynomials and modified Bessel functions of half-integral order
• Multidimensional Bell polynomials of higher order
• Laguerre-type Bell polynomials
• The umbral calculus
• Bell polynomials and differential equations of Freud-type polynomials
• An extension of the Bell polynomials
• Exponential polynomials
• Invariants orthogonaux pour certaines classes d'operateurs. (Orthogonal invariants for certain classes of operators)
• Some families of differential equations associated with the Hermite-based Appell polynomials and other classes of Hermite-based polynomials
• The Formula of FAA Di Bruno
• The Curious History of Faa di Bruno's Formula
• Symbolic computation of Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators
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