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An Extension of the Bell Polynomials
Computers and Mathematics With Applications, 2004 The authors introduce an extension of Bell polynomials, also called ``partition polynomials''. For a given integer \(M\) they define a generalized Bell polynomial \(Y_n^{[M-1]}\) as representing the \(n\)th derivative of the composite function \(\Phi(t) := f_{(1)}(f_{(2)}(\cdots(f_{(M)}(t))))\), where the functions \(f_{(M)}\), \dots, \(f_{(2)}\), \(f_{
P Natalini, P E Ricci
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General Identities on Bell Polynomials
Computers and Mathematics With Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiping Wang, Tianming Wang
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The Estimation of the Zeros of the Bell and r-Bell Polynomials
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
István Mező, Roberto B Corcino
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NONCOMMUTATIVE BELL POLYNOMIALS
International Journal of Algebra and Computation, 1996The recursive definition for the sequence of the Bell polynomials is generalized to noncommutative variables and then explicitly solved. As applications, we present formulas for the powers of a first-order matrix-valued differential operator, of the “substantial derivative” to a dynamical system, and for the Taylor coefficients of the time-ordered ...
Rainer Schimming, Saad Zagloul Rida
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International Journal of Computer Mathematics, 2010
The multivariate Bell polynomials are defined as the coefficients of a power of a multivariate series. We give recurrence relations for them and examples for dimensions 2 and 3.
Christopher S. Withers +1 more
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The multivariate Bell polynomials are defined as the coefficients of a power of a multivariate series. We give recurrence relations for them and examples for dimensions 2 and 3.
Christopher S. Withers +1 more
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A family of Apostol–Euler polynomials associated with Bell polynomials
Analysis, 2023Abstract Many authors investigated the characteristics of the Bell, Euler, Bernoulli, and Genocchi polynomials because of their numerous uses in statistics, number theory, and other branches of science. A generating function for mixed-type Apostol–Euler polynomials of order η related with Bell polynomials is presented in this study.
Nabiullah Khan, Saddam Husain
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ACM SIGSAM Bulletin, 1987
An introduction to Bell polynomials is given in order to see how they can be used to compute some of the classical counting functions of Combinatorics. They are also used to compute the Taylor coefficients of formal power series given as a composition of two power series along with computing the composition inverse of a power series.
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An introduction to Bell polynomials is given in order to see how they can be used to compute some of the classical counting functions of Combinatorics. They are also used to compute the Taylor coefficients of formal power series given as a composition of two power series along with computing the composition inverse of a power series.
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New Identities for the Partial Bell Polynomials
Applied Mathematics Letters, 2011 5 pages ...
Djurdje Cvijovic
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Bell Polynomials and Binomial Type Sequences
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Miloud Mihoubi
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Bell polynomials of arbitrary (fractional) orders+
Applied Mathematics and Computation, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. M. A. El-Sayed, Saad Zagloul Rida
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