Author
Yilmaz Simsek
Other affiliations: Mersin University, Uludağ University, Yahoo! ...read more
Bio: Yilmaz Simsek is an academic researcher from Akdeniz University. The author has contributed to research in topics: Bernoulli number & Orthogonal polynomials. The author has an hindex of 34, co-authored 237 publications receiving 4585 citations. Previous affiliations of Yilmaz Simsek include Mersin University & Uludağ University.
Papers published on a yearly basis
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TL;DR: In this article, the authors derived new identities related to the Frobenius-Euler polynomials and generalized Carliz's results. And they also gave a relation between the generalized Frobius Euler Polynomial and the generalized Hurwitz-Lerch zeta function at negative integers.
Abstract: The aim of this paper is to derive some new identities related to the Frobenius-Euler polynomials. We also give relation between the generalized Frobenius-Euler polynomials and the generalized Hurwitz-Lerch zeta function at negative integers. Furthermore, our results give generalized Carliz’s results which are associated with Frobenius-Euler polynomials. MSC:05A10, 11B65, 28B99, 11B68.
252 citations
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TL;DR: In this article, Wang et al. constructed uniform differentiable functions of the Bernoulli numbers and polynomials at negative integers, and proved analytic continuation of some basic (or $q$-) $L$% -series.
Abstract: By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions at negative integers are given explicitly. We also define new generating functions of $q$-Bernoulli numbers and polynomials. By using these functions, we prove analytic continuation of some basic (or $q$-) $L$% -series. These generating functions also interpolate Barnes' type Changhee $% q $-Bernoulli numbers with attached to Dirichlet character as well. By applying Mellin transformation, we obtain relations between Barnes' type $q$% -zeta function and new Barnes' type Changhee $q$-Bernolli numbers. Furthermore, we construct the Dirichlet type Changhee (or $q$-) $L$% -functions.
195 citations
TL;DR: In this article, by applying the Mellin transformation to these generating functions, they obtained integral representations of the new twisted (h, q ) -zeta function and twisted ( h, q )-L-function, which interpolate the twisted (H, q) -Bernoulli numbers and generalized twisted ( H, q ), q ) numbers at non-positive integers, respectively.
148 citations
01 Jan 2008
130 citations
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TL;DR: The Foundations of Statistics By Prof. Leonard J. Savage as mentioned in this paper, p. 48s. (Wiley Publications in Statistics.) Pp. xv + 294. (New York; John Wiley and Sons, Inc., London: Chapman and Hall, Ltd., 1954).
Abstract: The Foundations of Statistics By Prof. Leonard J. Savage. (Wiley Publications in Statistics.) Pp. xv + 294. (New York; John Wiley and Sons, Inc.; London: Chapman and Hall, Ltd., 1954.) 48s. net.
844 citations
744 citations
TL;DR: A Glimpse at Set Theory: The Topology of Cartesian Spaces and the Functions of One Variable.
Abstract: A Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in RP Integration in RP.
621 citations
TL;DR: One hundred years after the introduction of the Bernstein polynomial basis, this survey surveys the historical development and current state of theory, algorithms, and applications associated with this remarkable method of representing polynomials over finite domains.
451 citations