# 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)
The Euler-Maclaurin formula revisited. (English) Zbl 0928.65032

The author bases this paper on the conventional Euler-Maclaurin formula. The thrust of this paper is the evaluation of Cauchy principal value (CPV) integrals and for certain Hadamard finite part integrals (FPI). To this end he includes the extra term, introduced originally by the reviewer, for the CPV and differentiates the expansion, with respect to an incidental parameter, to obtain corresponding results for an FPI. He shows that the sigmoidal transformations (aka periodising transformations) are helpful in this context, and obtains discretization error estimates valid for functions belonging to a specified Sobolev space. The author points out that these results should prove particularly useful in the context of the solution of integral equations.

Although this paper appears in the journal immediately before a companion paper [the author, ibid. Ser. B 40, No. E, E77–E137 (1998; reviewed below)] on sigmoidal functions, it should clearly be read after the companion paper.

##### MSC:
 65D32 Quadrature and cubature formulas (numerical methods) 65B15 Euler-Maclaurin formula (numerical analysis) 41A55 Approximate quadratures