Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0940.11009
Huang, I-Chiau; Huang, Su-Yun
Bernoulli numbers and polynomials via residues. (English)
[J] J. Number Theory 76, No.2, 178-193 (1999). ISSN 0022-314X; ISSN 1096-1658/e

In the ring ${\Bbb Q}[[T]]$ of formal power series the authors study the subring generated by ${\Bbb Q}, T$ and $T/(e^T-1)$ together with the differential operator $T(d/dT)$. Using their calculus of generalized fractions and residues they show that the Bernoulli numbers $B^{(n)}_i$ of order $n$ and Bernoulli polynomials $B^{(n)}_i(X)$ can be realized as the residue of some suitable generalized fractions. Furthermore, they derive formulas of complete summations similar to $$ \sum_{i_1+\cdots+i_m=n}{n\choose{i_1,\ldots,i_m}} N_1^{i_1}\cdots N_m^{i_m}B_{i_1}(\alpha_1)\cdots B_{i_m}(\alpha_m), $$ where $\alpha_1,\ldots,\alpha_m$ are given rational numbers and $N_1,\ldots, N_m, m, n$ are positive numbers. Various known identities are derived, see {\it K. Dilcher} [J. Number Theory 60, 23-41 (1996; Zbl 0863.11011)] or {\it M. Eie} [Trans. Am. Math. Soc. 348, 1117-1136 (1996; Zbl 0864.11043)].
[Helmut Müller (Hamburg)]

MSC 2000:: *11B68 Bernoulli numbers, etc.

Keywords: Bernoulli numbers; Bernoulli polynomials; generalized fractions; formal power series ring

Citations: Zbl 0863.11011; Zbl 0864.11043

Cited in: Zbl 1091.11007 Zbl 1049.11020 Zbl 1042.11013

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]