Results 21 to 30 of about 706 (88)

Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind

Demonstratio Mathematica, 2022
In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan, Wu Lan, Lim Dongkyu, Qi Feng   +3 more
doaj   +1 more source

Some identities on Bernstein polynomials associated with q-Euler polynomials [PDF]

, 2011
In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.Comment: 8 ...
Bayad, Abdelmejid, Kim, Taekyun, Lee, Byunje, Rim, Seog-Hoon   +3 more
core   +4 more sources

A note on degenerate Hermite poly-Bernoulli numbers and polynomials

, 2016
In this paper, we introduce a new class of degenerate Hermite poly-Bernoulli polynomials and give some identities of these polynomials related to the Stirling numbers of the second kind.
W. Khan
semanticscholar   +1 more source

Explicit Formulas involving q-Euler Numbers and Polynomials [PDF]

, 2012
In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator.
Acikgoz, Mehmet, Araci, Serkan, Seo, Jong Jin   +2 more
core   +4 more sources

A note on the values of the weighted q-Bernstein polynomials and modified q-Genocchi numbers with weight alpha and beta via the p-adic q-integral on Zp [PDF]

, 2012
The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers.
DS Kim, HM Srivastava, HM Srivastava, IN Cangul, M Acikgoz, Mehmet Açikgöz, S Araci, S Araci, S Araci, S Araci, S Araci, S Araci, S-H Rim, Serkan Araci, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, T Kim, Y Simsek, Y Simsek   +25 more
core   +2 more sources

SIMPLIFICATION OF COEFFICIENTS IN DIFFERENTIAL EQUATIONS ASSOCIATED WITH HIGHER ORDER FROBENIUS – EULER NUMBERS

, 2017
In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and ...
Feng Qi (祁锋), Da-Wei Niu, Bai-Ni Guo (郭白妮)   +2 more
semanticscholar   +1 more source

A new approach to the r-Whitney numbers by using combinatorial differential calculus

Acta Universitatis Sapientiae: Mathematica, 2019
In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}.
Méndez Miguel A., Ramírez José L.
doaj   +1 more source

Sums of Powers and Special Polynomials

Discussiones Mathematicae - General Algebra and Applications, 2020
In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their ...
Boyadzhiev Khristo N.
doaj   +1 more source

An explicit formula for computing Bell numbers in terms of Lah and Stirling numbers [PDF]

Mediterranean Journal of Mathematics 13 (2016), no. 5, 2795--2800, 2014
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.
arxiv   +1 more source

SOME REMARKS ABOUT STIRLING NUMBERS OF THE SECOND KIND

Human Research in Rehabilitation, 2013
In this paper we give a representation of Stirling numbers of the second kind, we obtain explicit formulas for some cases of Stirling numbers of the second kind and illustrate a method for founding other such formulas.
Ramiz Vugdalić, Fatih Destović
doaj   +2 more sources