%0 Journal Article %T Fourier series of sums of products of poly-Bernoulli functions and their applications %A Kim, Taekyun %A Kim, Dae San %A Dolgy, Dmitry V. %A Park, Jin-Woo %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 5 %@ ISSN 2008-1901 %F Kim2017 %X In this paper, we consider three types of sums of products of poly-Bernoulli functions and derive Fourier series expansions of them. In addition, we express those three types of functions in terms of Bernoulli functions. %9 journal article %R 10.22436/jnsa.010.05.10 %U http://dx.doi.org/10.22436/jnsa.010.05.10 %P 2384--2401 %0 Journal Article %T On poly-Bernoulli numbers %A T. Arakawa %A M. Kaneko %J Comment. Math. Univ. St. Paul. %D 1999 %V 48 %F Arakawa1999 %0 Journal Article %T Multiple polylogarithms and multi-poly-Bernoulli polynomials %A A. Bayad %A Y. Hamahata %J Funct. Approx. Comment. Math. %D 2012 %V 46 %F Bayad2012 %0 Journal Article %T Degenerate poly-Bernoulli polynomials of the second kind %A D. V. Dolgy %A D. S. Kim %A T. Kim %A T. Mansour %J J. Comput. Anal. Appl. %D 2016 %V 21 %F Dolgy2016 %0 Journal Article %T Bernoulli number identities from quantum field theory and topological string theory %A G. V. Dunne %A C. Schubert %J Commun. Number Theory Phys. %D 2013 %V 7 %F Dunne2013 %0 Journal Article %T Hodge integrals and Gromov-Witten theory %A C. Faber %A R. Pandharipande %J Invent. Math. %D 2000 %V 139 %F Faber2000 %0 Journal Article %T On Miki’s identity for Bernoulli numbers %A I. M. Gessel %J J. Number Theory %D 2005 %V 110 %F Gessel2005 %0 Journal Article %T Poly-Bernoulli numbers %A M. Kaneko %J J. Théor. Nombres Bordeaux %D 1997 %V 9 %F Kaneko1997 %0 Journal Article %T Some formulae for the product of two Bernoulli and Euler polynomials %A D. S. Kim %A D. V. Dolgy %A T. Kim %A S.-H. Rim %J Abstr. Appl. Anal. %D 2012 %V 2012 %F Kim2012 %0 Journal Article %T Bernoulli basis and the product of several Bernoulli polynomials %A D. S. Kim %A T. Kim %J Int. J. Math. Math. Sci. %D 2012 %V 2012 %F Kim2012 %0 Journal Article %T Some identities of higher order Euler polynomials arising from Euler basis %A D. S. Kim %A T. Kim %J Integral Transforms Spec. Funct. %D 2013 %V 24 %F Kim2013 %0 Journal Article %T A note on degenerate poly-Bernoulli numbers and polynomials %A D. S. Kim %A T. Kim %J Adv. Difference Equ. %D 2015 %V 2015 %F Kim2015 %0 Journal Article %T A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials %A D. S. Kim %A T. Kim %J Russ. J. Math. Phys. %D 2015 %V 22 %F Kim2015 %0 Journal Article %T Higher-order Bernoulli and poly-Bernoulli mixed type polynomials %A D. S. Kim %A T. Kim %J Georgian Math. J. %D 2015 %V 22 %F Kim2015 %0 Journal Article %T Degenerate poly-Bernoulli polynomials with umbral calculus viewpoint %A D. S. Kim %A T. Kim %A H. I. Kwon %A T. Mansour %J J. Inequal. Appl. %D 2015 %V 2015 %F Kim2015 %0 Journal Article %T Fully degenerate poly-Bernoulli polynomials with a q parameter %A D. S. Kim %A T. Kim %A T. Mansour %A J.-J. Seo %J Filomat %D 2016 %V 30 %F Kim2016 %0 Journal Article %T Fourier series of higher-order Bernoulli functions and their applications %A T. Kim %A D. S. Kim %A S.-H. Rim %A D. V. Dolgy %J J. Inequal. Appl. %D 2017 %V 2017 %F Kim2017 %0 Journal Article %T Fully degenerate poly-Bernoulli numbers and polynomials %A T. Kim %A D. S. Kim %A J.-J. Seo %J Open Math. %D 2016 %V 14 %F Kim2016 %0 Journal Article %T Elementary classical analysis %A J. E. Marsden %J With the assistance of Michael Buchner, Amy Erickson, Adam Hausknecht, Dennis Heifetz, Janet Macrae and William Wilson, and with contributions by Paul Chernoff, Istv´an F´ary and Robert Gulliver, W. H. Freeman and Co., San Francisco %D 1974 %V %F Marsden1974 %0 Journal Article %T An application of p-adic convolutions %A K. Shiratani %A S. Yokoyama %J Mem. Fac. Sci. Kyushu Univ. Ser. A %D 1982 %V 36 %F Shiratani1982 %0 Journal Article %T Bernoulli and poly-Bernoulli polynomial convolutions and identities of p-adic Arakawa-Kaneko zeta functions %A P. T. Young %J J. Number Theory %D 2016 %V 12 %F Young2016 %0 Book %T Advanced engineering mathematics, second edition %A D. G. Zill %A M. R. Cullen %D 2000 %I Jones & Bartlett Learning %C Massachusetts %F Zill2000