论文信息 - An extension of the Euler-Maclaurin quadrature formula using a parametric type of Bernoulli polynomials

An extension of the Euler-Maclaurin quadrature formula using a parametric type of Bernoulli polynomials

Abstract In this paper, we introduce a parametric type of Bernoulli polynomials and study their basic properties in order to establish an extension of Euler-Maclaurin quadrature rules and compare them with the well-known ordinary case.

Wolfram Koepf | Mohammad Masjed-Jamei | M. R. Beyki | W. Koepf | M. Masjed‐Jamei

[1] M. Coppo,et al. The Arakawa–Kaneko zeta function , 2010 .

[2] S. Akiyama,et al. Multiple Zeta Values at Non-Positive Integers , 2001 .

[3] Mourad Rahmani,et al. On p-Bernoulli numbers and polynomials , 2015 .

[4] Y. Sasaki. On generalized poly-Bernoulli numbers and related L-functions , 2012 .

[5] M. Taqqu,et al. Noncentral Limit Theorems and Appell Polynomials , 1987 .

[6] Renzo Sprugnoli,et al. The Cauchy numbers , 2006, Discret. Math..

[7] M. Rahmani. The Akiyama–Tanigawa matrix and related combinatorial identities , 2013 .

[8] Kwang-Wu Chen,et al. Algorithms for Bernoulli numbers and Euler numbers , 2001 .

[9] Formal groups, Bernoulli-type polynomials and L-series , 2007 .

[10] R. Corcino,et al. Explicit formula for generalization of poly-Bernoulli numbers and polynomials with a,b,c parameters , 2011, 1109.1387.

[11] Y. Hamahata,et al. Special multi-poly-Bernoulli numbers. , 2007 .

[12] J. Stoer,et al. Introduction to Numerical Analysis , 2002 .

[13] Wolfram Koepf,et al. Symbolic computation of some power-trigonometric series , 2017, J. Symb. Comput..

[14] Niki Myrto Mavraki. Formal Groups , 2013 .

[15] Y. Hamahata,et al. POLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS , 2011 .