About: Hankel contour

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In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to(+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values of x. The Hankel contour can also be represented by a path that has mirror images just above and below the real axis, connected to a circle of radius ε, centered at the origin, where ε is an arbitrarily small number. The two linear portions of the contour are said to be a distance of δ from the real axis. Thus, the total distance between the linear portions of the contour is 2δ. The contour is traversed in the positively-oriented sense, meaning that the circle around the origin

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rdf:type	place yago:WikicatSpecialFunctions yago:Abstraction100002137 yago:Function113783816 yago:MathematicalRelation113783581 yago:Relation100031921
rdfs:label	Hankel contour (en)
rdfs:comment	In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to(+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values of x. The Hankel contour can also be represented by a path that has mirror images just above and below the real axis, connected to a circle of radius ε, centered at the origin, where ε is an arbitrarily small number. The two linear portions of the contour are said to be a distance of δ from the real axis. Thus, the total distance between the linear portions of the contour is 2δ. The contour is traversed in the positively-oriented sense, meaning that the circle around the origin (en)
foaf:depiction
dcterms:subject	Complex analysis Special functions
Wikipage page ID	1268560 (xsd:integer)
Wikipage revision ID	1031354107 (xsd:integer)
Link from a Wikipage to another Wikipage	Riemann zeta function Complex number Complex plane Mathematics Gamma function Differential equation Hermann Hankel Complex analysis Special functions Hugh Montgomery (mathematician) Methods of contour integration Counter clockwise Contour integral Real axis Hankel function Robert Charles Vaughan (mathematician)
Link from a Wikipage to an external page	https://dlmf.nist.gov/5.9 http://mathworld.wolfram.com/HankelContour.html
sameAs	Hankel contour Hankel contour Hankel contour Hankel contour Hankel contour
dbp:wikiPageUsesTemplate	dbt:Doi dbt:ISBN dbt:ISSN dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Hankel_Pic.png?width=300
has abstract	In mathematics, a Hankel contour is a path in the complex plane which extends from (+∞,δ), around the origin counter clockwise and back to(+∞,−δ), where δ is an arbitrarily small positive number. The contour thus remains arbitrarily close to the real axis but without crossing the real axis except for negative values of x. The Hankel contour can also be represented by a path that has mirror images just above and below the real axis, connected to a circle of radius ε, centered at the origin, where ε is an arbitrarily small number. The two linear portions of the contour are said to be a distance of δ from the real axis. Thus, the total distance between the linear portions of the contour is 2δ. The contour is traversed in the positively-oriented sense, meaning that the circle around the origin is traversed counter-clockwise. Use of Hankel contours is one of the methods of contour integration. This type of path for contour integrals was first used by Hermann Hankel in his investigations of the Gamma function. The Hankel contour is used to evaluate integrals such as the Gamma function, the Riemann zeta function, and other Hankel functions (which are Bessel functions of the third kind). (en)
gold:hypernym	Path
prov:wasDerivedFrom	wikipedia-en:Hankel_contour?oldid=1031354107&ns=0
page length (characters) of wiki page	4451 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Hankel_contour
is Link from a Wikipage to another Wikipage of	Riemann zeta function Contour integration Generating function transformation Gamma function Lerch zeta function Hermann Hankel Hurwitz zeta function Polylogarithm Reciprocal gamma function Stable count distribution
is foaf:primaryTopic of	wikipedia-en:Hankel_contour

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