Higher order bell polynomials and the relevant integer sequences

DOI10.2298/AADM1702327NzbMath1499.05021OpenAlexW2765833390WikidataQ60692737 ScholiaQ60692737MaRDI QIDQ5034293

Paolo Emilio Ricci, Pierpaolo Natalini

Publication date: 24 February 2022

Published in: Applicable Analysis and Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/aadm1702327n

zbMATH Keywords

partitionsBell polynomialscombinatorial analysisdifferentiation of composite functionshigher-order Bell polynomials and number

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Elementary theory of partitions (11P81) One-variable calculus (26A06)

Related Items (9)

Several explicit and recursive formulas for generalized Motzkin numbers ⋮ Bell polynomials and generalized Laplace transforms ⋮ Unnamed Item ⋮ Explicit formulas and recurrence relations for generalized Catalan numbers ⋮ 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 ⋮ Unnamed Item ⋮ New Bell-Sheffer polynomial sets

Uses Software

• Mathematica
• OEIS

Cites Work

• 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
• Invariants orthogonaux pour certaines classes d'operateurs. (Orthogonal invariants for certain classes of operators)
• The Formula of FAA Di Bruno
• Remarks on Bell and higher order Bell polynomials and numbers
• Symbolic computation of Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators
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