Closed formulas and identities on the Bell polynomials and falling factorials

Feng Qi; Da-Wei Niu; Dongkyu Lim; Bai-Ni Guo

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Closed formulas and identities on the Bell polynomials and falling factorials

机译：封闭式公式和钟多项式和下降阶乘的身份

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The authors establish a pair of closed-form expressions for special values of the Bell polynomials of the second kind for the falling factorials, derive two pairs of identities involving the falling factorials, find an equivalent expression between two special values for the Bell polynomials of the second kind, and present five closed-form expressions for the (modified) spherical Bessel functions.

机译：作者为下降阶乘的第二类钟多项式的特殊价值建立了一对闭合形式的表达，从而得出了两对涉及下降阶乘的身份，找到了两对特殊值之间的相当表达的钟多项式第二种，并为（改进的）球形贝塞尔功能提供五种闭合表达式。

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《Contributions to Discrete Mathematics》 |2020年第1期|共12页
作者
Feng Qi; Da-Wei Niu; Dongkyu Lim; Bai-Ni Guo;
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closed-form expressionBell polynomial of the second kindfalling factorialspecial valueidentityequivalent expressionspherical Bessel functionmodified spherical Bessel functionFa`a di Bruno formul;

机译：第二次幼仔闭合因子价值高度值的闭合形式的表达百分点表达式的表达式的球形贝塞尔函数模型球形贝塞尔Functionfa`a di bruno formul;

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1. Identities of Symmetry for Degenerate Euler Polynomials and Alternating Generalized Falling Factorial Sums [J] . Kim Taekyun, Kim Dae San Iranian Journal of Science and Technology. Transaction A, Science . 2017,第a4期

机译：退化的Euler多项式和交替的广义下降因子和的对称性
2. Identities for partial Bell polynomials derived from identities for weighted integer compositions [J] . Eger Steffen Aequationes mathematicae . 2016,第2期

机译：从加权整数组合的恒等式导出的贝尔部分多项式的恒等式
3. Extended Degenerate r -Central Factorial Numbers of the Second Kind and Extended Degenerate r -Central Bell Polynomials [J] . Dae San Kim, Dmitry V. Dolgy, Taekyun Kim, Symmetry . 2019,第4期

机译：第二类的扩展的简并的r-中心阶数和扩展的简并的r-中心贝尔多项式
4. Improved Polynomial Identity Testing for Read-Once Formulas [C] . Amir Shpilka, Ilya Volkovich Approximation, randomization, and combinatorial optimization : Algorithms and techniques . 2009

机译：改进的一次性公式多项式身份测试
5. Construction of designs in the presence of polynomial trends for varietal or factorial experiments. [D] . Lin, Meily. 1989

机译：在存在用于多项式或阶乘实验的多项式趋势的设计的构造。
6. Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube [O] . Dong Yun Shin, Sabir Hussain, Farkhanda Afzal, 2020

机译：采用M-Polynomial和Boron Trigular Nanotube的一些基于新程度的拓扑描述符的封闭式公式
7. Relations among Bell polynomials, central factorial numbers, and central Bell polynomials [O] . Feng Qi, Bai-Ni Guo 2019

机译：钟多项式，中央因子和中央钟多项式之间的关系

Closed formulas and identities on the Bell polynomials and falling factorials

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