Some results on power sums and Apostol-type polynomials

In this paper, we study the Apostol–Bernoulli polynomials, the Apostol–Euler polynomials and the power sums with respect to λ. As a result, various identities are established, including the multiplication formulae of the Apostol-type polynomials, some symmetric identities and some convolution identities.

[1]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[2]  K. S. Kölbig,et al.  Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints , 1972 .

[3]  Elias Deeba,et al.  Stirling's series and Bernoulli numbers , 1991 .

[4]  Hari M. Srivastava,et al.  Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials , 2005 .

[5]  Taekyun Kim,et al.  Symmetry p-adic invariant integral on ℤ p for Bernoulli and Euler polynomials , 2007, 0712.0138.

[6]  Tianming Wang,et al.  Some results on the Apostol-Bernoulli and Apostol-Euler polynomials , 2008, Comput. Math. Appl..

[7]  Hari M. Srivastava,et al.  Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials , 2006, Comput. Math. Appl..

[8]  Paul Thomas Young,et al.  Degenerate Bernoulli polynomials, generalized factorial sums, and their applications , 2008 .

[9]  Zhizheng Zhang,et al.  Several identities for the generalized Apostol-Bernoulli polynomials , 2008, Comput. Math. Appl..

[10]  F. T. Howard.  Applications of a Recurrence for the Bernoulli Numbers , 1995 .

[11]  Tom M. Apostol,et al.  On the Lerch zeta function. , 1951 .

[12]  Hari M. Srivastava,et al.  Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function , 2008, Appl. Math. Comput..

[13]  Qiu-Ming Luo,et al.  APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER AND GAUSSIAN HYPERGEOMETRIC FUNCTIONS , 2006 .

[14]  Weiping Wang,et al.  Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums , 2009, Discret. Math..

[15]  Hari M. Srivastava,et al.  Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions , 2006 .

[16]  Sheng-Liang Yang,et al.  An identity of symmetry for the Bernoulli polynomials , 2008, Discret. Math..

[17]  Hans J. H. Tuenter,et al.  A Symmetry of Power Sum Polynomials and Bernoulli Numbers , 2001, Am. Math. Mon..

[18]  Qiu-Ming Luo.  On the apostol-bernoulli polynomials , 2004 .

[19]  Kazuya Kato,et al.  Number Theory 1 , 1999 .