Results 21 to 30 of about 729 (84)

Construction a new generating function of Bernstein type polynomials

, 2010
Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given.
Simsek, Yilmaz
core   +1 more source

q-analogue of Euler-Barnes' numbers and polynomials

, 2005
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.Comment: 9 ...
Jang, Lee-Chae, Kim, Taekyun
core   +2 more sources

A study on a type of degenerate poly-Dedekind sums

Demonstratio Mathematica
Dedekind sums and their generalizations are defined in terms of Bernoulli functions and their generalizations. As a new generalization of the Dedekind sums, the degenerate poly-Dedekind sums, which are obtained from the Dedekind sums by replacing ...
Ma Yuankui, Luo Lingling, Kim Taekyun, Li Hongze, Zhang Wenpeng   +4 more
doaj   +1 more source

Analytic Continuation of weighted q-Genocchi numbers and polynomials

, 2012
In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function {\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n | {\alpha}) is derived ...
Acikgoz, Mehmet, Araci, Serkan, Gursul, Aynur   +2 more
core   +1 more source

Orthogonalizing q-Bernoulli polynomials

Demonstratio Mathematica
In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OBn(x,q){{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials.
Kuş Semra, Tuglu Naim
doaj   +1 more source

Proof of a congruence for harmonic numbers conjectured by Z.-W. Sun

, 2012
For a positive integer $n$ let $H_n=\sum_{k=1}^{n}1/k$ be the $n$th harmonic number. In this note we prove that for any prime $p\ge 7$, $$ \sum_{k=1}^{p-1}\frac{H_k^2}{k^2} \equiv4/5pB_{p-5}\pmod{p^2}, $$ which confirms the conjecture recently ...
Mestrovic, Romeo
core   +1 more source

Bernoulli type polynomials on Umbral Algebra

, 2011
The aim of this paper is to investigate generating functions for modification of the Milne-Thomson's polynomials, which are related to the Bernoulli polynomials and the Hermite polynomials. By applying the Umbral algebra to these generating functions, we
G Bretti, G Dattoli, L M Milne-Thomson, M-S Kim, P Blasiak, R Dere, R. Dere, S Roman, Y. Simsek   +8 more
core   +1 more source

Monotonicity, convexity, and Maclaurin series expansion of Qi's normalized remainder of Maclaurin series expansion with relation to cosine

Open Mathematics
In this article, the authors introduce Qi’s normalized remainder of the Maclaurin series expansion of Qi’s normalized remainder for the cosine function.
Pei Wei-Juan, Guo Bai-Ni
doaj   +1 more source

Asymptotic approximations of Apostol-Frobenius-Euler polynomials of order α in terms of hyperbolic functions

Demonstratio Mathematica
The study of special functions has become an enthralling area in mathematics because of its properties and wide range of applications that are relevant into other fields of knowledge.
Corcino Cristina B., Castañeda Wilson D., Corcino Roberto B.   +2 more
doaj   +1 more source

Averages of Ramanujan sums: Note on two papers by E. Alkan

, 2014
We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms ...
Tóth, László
core   +1 more source