Multidimensional Bell polynomials of higher order

DOI10.1016/j.camwa.2005.05.008zbMath1113.33025OpenAlexW2038288337MaRDI QIDQ814125

Paolo Emilio Ricci, Angela Bernardini, Pierpaolo Natalini

Publication date: 2 February 2006

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2005.05.008

zbMATH Keywords

symmetric functionsBell polynomialsdifferentiation of composite functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Other functions coming from differential, difference and integral equations (33E30) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50)

Related Items (21)

Higher order bell polynomials and the relevant integer sequences ⋮ New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two-Boson Equation ⋮ Bell polynomials and generalized Laplace transforms ⋮ Unnamed Item ⋮ Laguerre-type Bell polynomials ⋮ Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and total variation spaces ⋮ The \(n\)th order implicit differentiation formula for two variables with an application to computing all roots of a transcendental function ⋮ General Sets of Bell-Sheffer and Log-Sheffer Polynomials ⋮ A unified approach to some recurrence sequences via Faà di Bruno's formula ⋮ Bell polynomials and modified Bessel functions of half-integral order ⋮ Bell-Sheffer exponential polynomials of the second kind ⋮ Bell polynomials and generalized Blissard problems ⋮ General identities on Bell polynomials ⋮ Some extensions of Faà di Bruno's formula with divided differences ⋮ Remarks on Bell and higher order Bell polynomials and numbers ⋮ Logarithmic-Sheffer polynomials of the second kind ⋮ New Bell-Sheffer polynomial sets ⋮ Estimation of multivariate generalized gamma convolutions through Laguerre expansions ⋮ A new set of Sheffer-Bell polynomials and logarithmic numbers ⋮ Super extension of Bell polynomials with applications to supersymmetric equations ⋮ Unnamed Item

Cites Work

• 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
• Symbolic computation of Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators
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