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#### A note on the new extended beta and gauss hypergeometric functions

(Natural Sciences Publishing USA, 2018-01-01)

A variety of extensions of the classical beta function and the Gauss hypergeometric function 2F1 have been presented and investigated. In this sequel, we aim to give a further extension of the extended beta function, which ...

#### Modified Stancu operators based on inverse Polya Eggenberger distribution

(SPRINGER INTERNATIONAL PUBLISHING AG, 2017-03-06)

In this paper, we construct a sequence of modified Stancu-Baskakov operators for a real valued function bounded on [0, infinity), based on a function tau (x). This function tau (x) is infinite times continuously differentiable ...

#### ON A p-ADIC INTERPOLATING FUNCTION FOR THE GENERALIZED GENOCCHI NUMBERS AND ITS BEHAVIOUR AT s=0

(CHARLES BABBAGE RES CTR, 2015-07)

In this work, we consider the generalized Genocchi numbers and polynomials. However, we introduce analytic interpolating function for the generalized Genocchi numbers attached to chi at negative integers in complex plane ...

#### Linking of Bernstein-Chlodowsky and Szasz-Appell-Kantorovich type operators

(INT SCIENTIFIC RESEARCH PUBLICATIONS, 2017)

In the present paper, we define a sequence of bivariate operators by linking the Bernstein-Chlodowsky operators and the Szasz-Kantorovich operators based on Appell polynomials. First, we establish the moments of the operators ...

#### Blending type approximation by Stancu-Kantorovich operators based on Polya-Eggenberger distribution

(DE GRUYTER OPEN LTD, 2017)

In the paper the authors introduce the Kantorovich variant of Stancu operators based on Polya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with ...

#### A novel approach for obtaining new identities for the lambda extension of q- Euler polynomials arising from the q-umbral calculus

(INT SCIENTIFIC RESEARCH PUBLICATIONS, 2017)

In this article, a new q-generalization of the Apostol-Euler polynomials is introduced using the usual q-exponential function. We make use of such a generalization to derive several properties arising from the q-umbral ...

#### An analogue of Eulerian polynomials related to L-type function

(MAEJO UNIV, 2015-05)

We introduce Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-invairant integral in the p-adic integer ring and obtain some new interesting identities. Using a complex contour integral representation ...

#### Some new formulas for the products of the Apostol type polynomials

(SPRINGEROPEN, 2016-11-10)

In the year 2014, Kim et al. computed a kind of new sums of the products of an arbitrary number of the classical Bernoulli and Euler polynomials by using the Euler basis for the vector space of polynomials of bounded degree. ...

#### (ρ,q)-Volkenborn integration

(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017-02)

In the paper, we introduce an analogue of Haar distribution based on (rho, q)-numbers, as follows:
mu(rho,q) (a + p(N)Z(p)) = rho(pN)/[p(N)](rho,q) (q/rho)(a)
By means of this distribution, we derive (rho, q)-analogue ...

#### lambda-STATISTICAL CONVERGENCE OF BERNSTEIN POLYNOMIAL SEQUENCES

(MILI PUBL, 2017-01)

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the lambda-statistical convergence of sequence ...