Results 11 to 20 of about 1,461 (202)
A new approach to Bell and poly-Bell numbers and polynomials [PDF]
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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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 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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Some new formulas of complete and incomplete degenerate Bell polynomials [PDF]
Advances in Difference Equations, 2021 The aim of this paper is to study the complete and incomplete degenerate Bell polynomials, which are degenerate versions of the complete and incomplete Bell polynomials, and to derive some properties and identities for those polynomials.
Dae San Kim +3 more
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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 Identities of Degenerate Bell Polynomials [PDF]
Mathematics, 2020 The new type degenerate of Bell polynomials and numbers were recently introduced, which are a degenerate version of Bell polynomials and numbers and are different from the previously introduced partially degenerate Bell polynomials and numbers.
Taekyun Kim +3 more
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Congruences on the Bell polynomials and the derangement polynomials [PDF]
Journal of Number Theory, 2022 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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New Properties on Degenerate Bell Polynomials [PDF]
Complexity, 2021 The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate versions of the Bell numbers and polynomials. We derive some new identities and properties of those numbers and polynomials that are associated with the ...
Taekyun Kim +4 more
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Representations by ordered Bell and degenerate ordered Bell polynomials [PDF]
Rocky Mountain Journal of Mathematics, 2022 20 pages.
Dae san Kim, Taekyun Kim
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Fourier series of functions involving higher-order ordered Bell polynomials
Open Mathematics, 2017 In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the ...
Kim Taekyun +3 more
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