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Degenerate poly-Bell polynomials and numbers [PDF]
Advances in Difference Equations, 2021 Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such as Bernoulli, Euler, Cauchy, and Genocchi polynomials.
Taekyun Kim, Hye Kyung Kim
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Laguerre-type Bell polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite ...
P. Natalini, P. E. Ricci
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Complete and incomplete Bell polynomials associated with Lah–Bell numbers and polynomials [PDF]
Advances in Difference Equations, 2021 The nth r-extended Lah–Bell number is defined as the number of ways a set with n + r $n+r$ elements can be partitioned into ordered blocks such that r distinguished elements have to be in distinct ordered blocks.
Taekyun Kim +4 more
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Some properties of degenerate complete and partial Bell polynomials [PDF]
Advances in Difference Equations, 2021 In this paper, we study degenerate complete and partial Bell polynomials and establish some new identities for those polynomials. In addition, we investigate the connections between modified degenerate complete and partial Bell polynomials, which are ...
Taekyun Kim +4 more
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Some identities on truncated polynomials associated with Lah-Bell polynomials [PDF]
Applied Mathematics in Science and Engineering, 2023 Recently, Kim-Kim introduced the truncated degenerate Bell polynomials and numbers. In this paper, we introduce the truncated Lah-Bell polynomials and numbers. We obtain some identities, recurrence relations and properties. Furthermore, we also introduce
Lingling Luo +3 more
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A new approach to Bell and poly-Bell numbers and polynomials
AIMS Mathematics, 2022 Bell polynomials are widely applied in many problems arising from physics and engineering. The aim of this paper is to introduce new types of special polynomials and numbers, namely Bell polynomials and numbers of the second kind and poly-Bell ...
Taekyun Kim +4 more
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Congruences on the Bell polynomials and the derangement polynomials
Journal of Number Theory, 2010 In this note, by the umbra calculus method, the Sun and Zagier's congruences involving the Bell numbers and the derangement numbers are generalized to the polynomial cases. Some special congruences are also provided.
Yidong Sun, Xiaojuan Wu, Jujuan Zhuang
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Bell-Based Bernoulli Polynomials with Applications [PDF]
Axioms, 2021 In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind.
Ugur Duran, Serkan Araci, Mehmet Acikgoz
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Some Inequalities of the Bell Polynomials [PDF]
, 2017 In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds ...
Feng Qi
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The role of Bell polynomials in integration
Journal of Computational and Applied Mathematics, 2001 Abstract It is shown that, in the evaluation of certain integrals, the answer will be a simple multiple of a Bell polynomial. Integrals of the form I n,α,β ≔ ∫ 0 π /2 ln n ( sin α θ cos β θ) d θ , where n is a nonnegative integer, are provided as examples. We focus in particular on the integrals I
C. B. Collins
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