zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some identities for multiple zeta values. (English) Zbl 1229.11119

Summary: In this note, we obtain the following identities,

a+b+c=n ζ(2a,2b,2c)=5 8ζ(2n)-1 4ζ(2)ζ(2n-2),forn>2,
a+b+c+d=n ζ(2a,2b,2c,2d)=35 64ζ(2n)-5 16ζ(2)ζ(2n-2),forn>3,

Meanwhile, some weighted version of sum formulas are also obtained.


MSC:
11M32Multiple Dirichlet series, etc.
11B68Bernoulli and Euler numbers and polynomials
References:
[1]Chen, W. Y. C.; Sun, L. H.: Extended Zeilberger’s algorithm for identities on Bernoulli and Euler polynomials, J. number theory 129, 2111-2132 (2009) · Zbl 1183.11011 · doi:10.1016/j.jnt.2009.01.026
[2]Eie, M.: A note on Bernoulli numbers and shintani generalized Bernoulli polynomials, Trans. amer. Math. soc. 248, 1117-1136 (1996) · Zbl 0864.11043 · doi:10.1090/S0002-9947-96-01479-1
[3]Gangl, H.; Kaneko, M.; Zagier, D.: Double zeta values and modular forms, Automorphic forms and zeta functions. In memory of tsuneo arakawa, proc. Of the conf., 71-106 (2006)
[4]Granville, A.: A decomposition of Riemann’s zeta function, London math. Soc. lecture note ser. 247, 95-101 (1997) · Zbl 0907.11024
[5]Guo, L.; Xie, B.: Weighted sum formula for multiple zeta values, J. number theory 129, 2747-2765 (2009) · Zbl 1229.11117 · doi:10.1016/j.jnt.2009.04.018
[6]Nakamura, T.: Restricted and weighted sum formulas for double zeta values of even weight, Šiauliai math. Semin. 12, 151-155 (2009) · Zbl 1205.11099 · doi:http://siauliaims.su.lt/pdfai/2009/Nakamura-09.pdf
[7]Ohno, Y.; Zudilin, W.: Zeta stars, Commun. number theory phys. 2, 327-349 (2008)