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)
A new method in the study of Euler sums. (English) Zbl 1155.40002
Summary: A new method in the study of Euler sums is developed. A host of Euler sums, typically of the form n=1 f(n) n s m=1 n g(m) m t , are expressed in closed form. Also obtained as a by-product are some striking recursive identities involving several Dirichlet series including the well-known Riemann zeta function.

MSC:
40A25Approximation to limiting values (summation of series, etc.)
40B05Multiple sequences and series
11M99Analytic theory of zeta and L-functions
33E99Other special functions
References:
[1]Apostol, T.M., Vu, T.H.: Dirichlet Series related to the Riemann Zeta function. J. Number Theory 19, 85–120 (1984) · Zbl 0539.10032 · doi:10.1016/0022-314X(84)90094-5
[2]Bailey, D.H., Borwein, J.M., Girgensohn, R.: Experimental evaluation of Euler sums. Exp. Math. 3, 17–30 (1994)
[3]Basu, A., Apostol, Tom M.: A new method for investigating Euler sums. Ramanujan J. 4, 397–419 (2000) · Zbl 0971.40001 · doi:10.1023/A:1009868016412
[4]Crandall, R.E., Buhler, J.P.: On the evaluation Euler sums. Exp. Math. 3, 275–285 (1994)
[5]Ramanujan, S.: Note Books, vol. 2 (1957)
[6]Williams, G.T.: A method of evaluating ζ(2n). Am. Math. Mon. 60, 19–25 (1953) · Zbl 0050.06803 · doi:10.2307/2306473