Congruences for Generalized <inline-formula> <graphic file="1029-242X-2008-270713-i1.gif"/></inline-formula>-Bernoulli Polynomials

• Main Authors: Cenkci Mehmet, Kurt Veli
• Format: Article
• Language: English
• Published: SpringerOpen 2008-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2008/270713

<p>Abstract</p> <p>In this paper, we give some further properties of <inline-formula> <graphic file="1029-242X-2008-270713-i2.gif"/></inline-formula>-adic <inline-formula> <graphic file="1029-242X-2008-270713-i3.gif"/></inline-formula>-<inline-formula> <graphic file="1029-242X-2008-270713-i4.gif"/></inline-formula>-function of two variables, which is recently constructed by Kim (2005) and Cenkci (2006). One of the applications of these properties yields general classes of congruences for generalized <inline-formula> <graphic file="1029-242X-2008-270713-i5.gif"/></inline-formula>-Bernoulli polynomials, which are <inline-formula> <graphic file="1029-242X-2008-270713-i6.gif"/></inline-formula>-extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox (2000), Gunaratne (1995), and Young (1999, 2001).</p>