Hankel contour

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.

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 mirror image extending from −∞, circling the origin clockwise, and returning to −∞ is also called a Hankel contour.

References

Hugh L. Montgomery; Robert C. Vaughan (2007). Multiplicative number theory I. Classical theory. Cambridge tracts in advanced mathematics. 97. p. 515. ISBN 0-521-84903-9.

Mathematics Encyclopedia