A Further Symmetric Relation on the Analogue of the Apostol-Bernoulli and the Analogue of the Apostol-Genocchi Polynomials

The main object of this paper is to investigate some relations between the analogue of the Apostol-Bernoulli and the analogue of the Apostol-Genocchi polynomials. We first establish some relations between the analogue of the Apostol-Bernoulli and the analogue of the Apostol-Genocchi polynomials. Furthermore we give two symmetric relations on the analogue of the Apostol-Bernoulli and the analogue of the Apostol-Genocchi polynomials.

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

[2]  Hari M. Srivastava,et al.  Remarks on some relationships between the Bernoulli and Euler polynomials , 2004, Appl. Math. Lett..

[3]  Taekyun Kim.  q-Extension of the Euler formula and trigonometric functions , 2007 .

[4]  Cenkci Mehmet,et al.  q-EXTENSIONS OF GENOCCHI NUMBERS , 2006 .

[5]  Hans J. H. Tuenter.  The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers☆ , 2006 .

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

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

[8]  Gi-Sang Cheon,et al.  A note on the Bernoulli and Euler polynomials , 2003, Appl. Math. Lett..

[9]  Taekyun Kim.  On p-adic q-l-functions and sums of powers , 2007 .

[10]  Boris A Kupershmidt.  Reflection Symmetries of q-Bernoulli Polynomials , 2005 .

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

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

[13]  Ravi Kannan,et al.  The Frobenius Problem , 1989, FSTTCS.

[14]  Yilmaz Simsek,et al.  On twisted q-Hurwitz zeta function and q-two-variable L-function , 2007, Appl. Math. Comput..

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

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

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