Results 61 to 70 of about 1,405 (108)

New families of special numbers and polynomials arising from applications of p-adic q-integrals

Advances in Difference Equations, 2017
In this manuscript, generating functions are constructed for the new special families of polynomials and numbers using the p-adic q-integral technique. Partial derivative equations, functional equations and other properties of these generating functions ...
Daeyeoul Kim, Hacer Ozden Ayna, Yilmaz Simsek, Ahmet Yardimci   +3 more
doaj   +1 more source

Some identities of higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus [PDF]

, 2013
In this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have alternative ways ...
Dolgy, Dmitry v., Kim, Dae San, Kim, Taekyun, Rim, Seog-Hoon   +3 more
core  

Some Properties of Generalized Apostol-Type Frobenius–Euler–Fibonacci Polynomials

Mathematics
In this paper, by using the Golden Calculus, we introduce the generalized Apostol-type Frobenius–Euler–Fibonacci polynomials and numbers; additionally, we obtain various fundamental identities and properties associated with these polynomials and numbers,
Maryam Salem Alatawi, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo   +3 more
doaj   +1 more source

Some New Results Involving the Generalized Bose–Einstein and Fermi–Dirac Functions

Axioms, 2019
In this paper, we obtain a new series representation for the generalized Bose−Einstein and Fermi−Dirac functions by using fractional Weyl transform.
Rekha Srivastava, Humera Naaz, Sabeena Kazi, Asifa Tassaddiq   +3 more
doaj   +1 more source

Some Relationships between the Generalized Apostol-Bernoulli and Apostol-Euler Polynomials [PDF]

Turkish Journal of Analysis and Number Theory, 2016
The main objective of this paper is to introduce and investigate two new classes of generalized Apostol-Bernoulli polynomials B n [ m-1, α ] (x;c,α;λ) and Apostol-Euler polynomials e n [m-1, α ] (x;c,α;λ). In particular, we obtain addition formula for the new class of the generalized Apostol-Bernoulli polynomials.
openaire   +1 more source

Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

, 2015
In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis.
Acikgoz, Mehmet, Araci, Serkan, Bagdasaryan, Armen, He, Yuan   +3 more
core  

New recurrence formulae for the Apostol-Bernoulli and Apostol-Euler polynomials [PDF]

Advances in Difference Equations, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Identities on the k-ary Lyndon words related to a family of zeta functions

, 2016
The main aim of this paper is to investigate and introduce relations between the numbers of k-ary Lyndon words and unified zeta-type functions which was defined by Ozden et al [15, p. 2785].
Kucukoglu, Irem, Simsek, Yilmaz
core  

Degenerate Fubini-type polynomials associated with degenerate Apostol-Bernoulli and Apostol-Euler polynomials of order ��

, 2021
In this paper, by introducing the degenerate Fubini-type polynomials, we give several relations with the help of the Fa di Bruno formula and some properties of Bell polynomials, and generating function methods. Also, we derive some new explicit formulas and recurrence relations for Fubini-type polynomials and numbers.
openaire   +2 more sources

Fourier expansions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials [PDF]

Mathematics of Computation, 2011
We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.
openaire   +2 more sources