Results 171 to 180 of about 1,081 (189)

RESTRICTED r-BELL NUMBERS, POLYNOMIALS and (r; β)-BELL POLYNOMIALS

jnanabha
We prove the existence of maximal and minimal integrable solutions of nonlinear Urysohn type integral equations. Two basic integral inequalities are obtained in the form of extremal integrable solutions which are further exploited for proving the boundedness and uniqueness of the integrable solutions of the considered integral equation.
Pathan, M. A., Kumar, Hemant
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On hermite-bell inverse polynomials

Rendiconti del Circolo Matematico di Palermo, 1984
Bell introduced a set of polynomials by \[ \exp g(z)(d^ n/dz^ n)\exp [-g(z)]=Y_ n(g:z)\quad where\quad g(z)=\sum^{\infty}_{n=1}a_ nz^ n. \] In the present paper a related set of polynomials is considered for \(g(z)=pz^{-k}\), where p is a constant and K is a positive integer.
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A Note on Central Bell Numbers and Polynomials

Russian Journal of Mathematical Physics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, T., Kim, D. S.
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The Bell Differential Polynomials

1998
Let A be an associative algebra with a unit element 1. If A is commutative then there holds the well-known binomial law $$ (x + y)n = \sum\limits_{k = 0}^n {(_k^n} {)_x}n - {k_y}k $$ (1) where formally x 0 = 1, y 0 = 1. Our aim is to generalize the binomial law to the case where A is not necessarily commutative.
R. Schimming, S. Z. Rida
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Bivariate extension of Bell polynomials

J. Integer Seq., 2019
Let \(Y_n(x_1,\ldots,x_n)\) denote the (complete) Bell polynomials according to [\textit{J. Riordan}, An introduction to combinatorial analysis. London: Chapman \& Hall, Ltd (1958; Zbl 0078.00805), p. 35] and set \(B_n(x):=Y_n(x,\ldots,x)\). The starting point of the authors is \textit{M. Z. Spivey}'s recurrence formula for the Bell numbers \(B_n(1)\) [
Yuanping Zheng, Nadia N. Li
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Linear recurrences for \(r\)-Bell polynomials

J. Integer Seq., 2014
Summary: Letting \(B_{n,r}\) be the \(n\)-th \(r\)-Bell polynomial, it is well known that \(B_n(x)\) admits specific integer coordinates in the two bases \(\{x^i\}_i\) and \(\{xB_i(x)\}_i\) according to, respectively, the Stirling numbers and the binomial coefficients. Our aim is to prove that the sequences \(B_{n+m,r}(x)\) and \(B_{n,r+s}(x)\) admit a
Miloud Mihoubi 0002, Hacène Belbachir
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Some Identities of Extended Degenerate r-Central Bell Polynomials Arising From Umbral Calculus

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2020
Taekyun Kim, Dae San Kim
exaly  

Some Identities of Bell Polynomials

Science China Mathematics, 2015
Taekyun Kim, Dae San Kim
exaly  

Special Values of the Bell Polynomials of the Second Kind for Some Sequences and Functions

Journal of Mathematical Analysis and Applications, 2020
Feng Qi, Yonghong Yao, Dongkyu Lim
exaly  

On Central Complete and Incomplete Bell Polynomials I

Symmetry, 2019
Taekyun Kim, Dae San Kim, Gwan-Woo Jang
exaly