TY - JOUR AU - Kim, Taekyun AU - Kim, Dae San AU - Dolgy, Dmitry V. AU - Park, Jin-Woo PY - 2017 TI - Fourier series of sums of products of poly-Bernoulli functions and their applications JO - Journal of Nonlinear Sciences and Applications SP - 2384--2401 VL - 10 IS - 5 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.05.10 DO - 10.22436/jnsa.010.05.10 ID - Kim2017 ER - TY - JOUR TI - On poly-Bernoulli numbers AU - T. Arakawa AU - M. Kaneko JO - Comment. Math. Univ. St. Paul. PY - 1999 DA - 1999// VL - 48 ID - Arakawa1999 ER - TY - JOUR TI - Multiple polylogarithms and multi-poly-Bernoulli polynomials AU - A. Bayad AU - Y. Hamahata JO - Funct. Approx. Comment. Math. PY - 2012 DA - 2012// VL - 46 ID - Bayad2012 ER - TY - JOUR TI - Degenerate poly-Bernoulli polynomials of the second kind AU - D. V. Dolgy AU - D. S. Kim AU - T. Kim AU - T. Mansour JO - J. Comput. Anal. Appl. PY - 2016 DA - 2016// VL - 21 ID - Dolgy2016 ER - TY - JOUR TI - Bernoulli number identities from quantum field theory and topological string theory AU - G. V. Dunne AU - C. Schubert JO - Commun. Number Theory Phys. PY - 2013 DA - 2013// VL - 7 ID - Dunne2013 ER - TY - JOUR TI - Hodge integrals and Gromov-Witten theory AU - C. Faber AU - R. Pandharipande JO - Invent. Math. PY - 2000 DA - 2000// VL - 139 ID - Faber2000 ER - TY - JOUR TI - On Miki’s identity for Bernoulli numbers AU - I. M. Gessel JO - J. Number Theory PY - 2005 DA - 2005// VL - 110 ID - Gessel2005 ER - TY - JOUR TI - Poly-Bernoulli numbers AU - M. Kaneko JO - J. Théor. Nombres Bordeaux PY - 1997 DA - 1997// VL - 9 ID - Kaneko1997 ER - TY - JOUR TI - Some formulae for the product of two Bernoulli and Euler polynomials AU - D. S. Kim AU - D. V. Dolgy AU - T. Kim AU - S.-H. Rim JO - Abstr. Appl. Anal. PY - 2012 DA - 2012// VL - 2012 ID - Kim2012 ER - TY - JOUR TI - Bernoulli basis and the product of several Bernoulli polynomials AU - D. S. Kim AU - T. Kim JO - Int. J. Math. Math. Sci. PY - 2012 DA - 2012// VL - 2012 ID - Kim2012 ER - TY - JOUR TI - Some identities of higher order Euler polynomials arising from Euler basis AU - D. S. Kim AU - T. Kim JO - Integral Transforms Spec. Funct. PY - 2013 DA - 2013// VL - 24 ID - Kim2013 ER - TY - JOUR TI - A note on degenerate poly-Bernoulli numbers and polynomials AU - D. S. Kim AU - T. Kim JO - Adv. Difference Equ. PY - 2015 DA - 2015// VL - 2015 ID - Kim2015 ER - TY - JOUR TI - A note on poly-Bernoulli and higher-order poly-Bernoulli polynomials AU - D. S. Kim AU - T. Kim JO - Russ. J. Math. Phys. PY - 2015 DA - 2015// VL - 22 ID - Kim2015 ER - TY - JOUR TI - Higher-order Bernoulli and poly-Bernoulli mixed type polynomials AU - D. S. Kim AU - T. Kim JO - Georgian Math. J. PY - 2015 DA - 2015// VL - 22 ID - Kim2015 ER - TY - JOUR TI - Degenerate poly-Bernoulli polynomials with umbral calculus viewpoint AU - D. S. Kim AU - T. Kim AU - H. I. Kwon AU - T. Mansour JO - J. Inequal. Appl. PY - 2015 DA - 2015// VL - 2015 ID - Kim2015 ER - TY - JOUR TI - Fully degenerate poly-Bernoulli polynomials with a q parameter AU - D. S. Kim AU - T. Kim AU - T. Mansour AU - J.-J. Seo JO - Filomat PY - 2016 DA - 2016// VL - 30 ID - Kim2016 ER - TY - JOUR TI - Fourier series of higher-order Bernoulli functions and their applications AU - T. Kim AU - D. S. Kim AU - S.-H. Rim AU - D. V. Dolgy JO - J. Inequal. Appl. PY - 2017 DA - 2017// VL - 2017 ID - Kim2017 ER - TY - JOUR TI - Fully degenerate poly-Bernoulli numbers and polynomials AU - T. Kim AU - D. S. Kim AU - J.-J. Seo JO - Open Math. PY - 2016 DA - 2016// VL - 14 ID - Kim2016 ER - TY - JOUR TI - Elementary classical analysis AU - J. E. Marsden JO - 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 PY - 1974 DA - 1974// VL - ID - Marsden1974 ER - TY - JOUR TI - An application of p-adic convolutions AU - K. Shiratani AU - S. Yokoyama JO - Mem. Fac. Sci. Kyushu Univ. Ser. A PY - 1982 DA - 1982// VL - 36 ID - Shiratani1982 ER - TY - JOUR TI - Bernoulli and poly-Bernoulli polynomial convolutions and identities of p-adic Arakawa-Kaneko zeta functions AU - P. T. Young JO - J. Number Theory PY - 2016 DA - 2016// VL - 12 ID - Young2016 ER - TY - BOOK TI - Advanced engineering mathematics, second edition AU - D. G. Zill AU - M. R. Cullen PB - Jones & Bartlett Learning PY - 2000 DA - 2000// CY - Massachusetts ID - Zill2000 ER -