NDLI: A New Approach to <inline-formula><graphic file="1687-1847-2010-951764-i1.gif"/></inline-formula>-Bernoulli Numbers and <inline-formula><graphic file="1687-1847-2010-951764-i2.gif"/></inline-formula>-Bernoulli Polynomials Related to <inline-formula><graphic file="1687-1847-2010-951764-i3.gif"/></inline-formula>-Bernstein Polynomials

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A New Approach to -Bernoulli Numbers and -Bernoulli Polynomials Related to -Bernstein Polynomials

Content Provider	Directory of Open Access Journals (DOAJ)
Author	Açikgöz Mehmet Erdal Dilek Araci Serkan
Abstract	We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials. We also consider the generalized -Bernoulli polynomials attached to Dirichlet's character and have their generating function . We obtain distribution relations for the -Bernoulli polynomials and have some identities involving -Bernoulli numbers and polynomials related to the second kind Stirling numbers and -Bernstein polynomials. Finally, we derive the -extensions of zeta functions from the Mellin transformation of this generating function which interpolates the -Bernoulli polynomials at negative integers and is associated with -Bernstein polynomials.
Related Links	http://www.advancesindifferenceequations.com/content/2010/951764
ISSN	16871839
e-ISSN	16871847
Journal	Advances in Difference Equations
Issue Number	1
Volume Number	2010
Language	English
Publisher	SpringerOpen
Publisher Date	2010-01-01
Publisher Place	United Kingdom
Access Restriction	Open
Subject Keyword	Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Algebra and Number Theory Analysis

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