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)
Harmonic sums, Mellin transforms and integrals. (English) Zbl 0939.65032

The computation of Feynman diagrams has confronted physicists with classes of integrals that are usually hard to be evaluated, both analytically and numerically. Also the newer techniques applied in the more popular computer algebra packages do not offer much relief. Therefore it is good to occasionally study some alternative methods to come to a result. In the case of the computation of structure functions in deep inelastic scattering one is often interested in their Mellin moments. It treats Mellin transforms and inverse Mellin transformation for functions that are encountered in Feynman diagram calculations. This paper also describes algorithms to deal with nested symbolic sums over combinations of harmonic series, binomial coefficients and denominators. Also many sums that had to be evaluated seem to involve new results. Most of the algorithms have been programmed in the language of FORM. The resulting set of procedures is called SUMMER.

This paper contains a number of appendices. Additionally there is an appendix with lists of symbolic sums that are not directly treated by the general algorithm.


MSC:
65D32Quadrature and cubature formulas (numerical methods)
65B10Summation of series (numerical analysis)
65R10Integral transforms (numerical methods)
44A15Special transforms (Legendre, Hilbert, etc.)
65Z05Applications of numerical analysis to physics
81T18Feynman diagrams
81-08Computational methods (quantum theory)
65D20Computation of special functions, construction of tables