Talk:Hankel contour

Wiki Education Foundation-supported course assignment

This article was the subject of a Wiki Education Foundation-supported course assignment, between 26 August 2019 and 10 December 2019. Further details are available on the course page. Student editor(s): S. Westaway.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 23:03, 16 January 2022 (UTC)[reply]

References

I've added one from Montgomery and Vaughan, which I happen to have by me, but would prefer something better. Richard Pinch (talk) 20:30, 8 September 2008 (UTC)[reply]

I've added a few in that make use of the Hankel contour, they've also been cited within the article. S. Westaway (talk) 21:14, 27 November 2019 (UTC)[reply]

Clarification of the Hankel Contour as stated within the article

When I have been introduced to the Hankel contour it has been as two lines (one above the Real axis in the Complex Plane and one below the Real axis in the Complex Plane) connected by the arc of a circle. This is definitely NOT what the picture shows, and I believe there may be a minor error with the sign of the Delta in the main article. The point at which the arc of the circle intersects the line above the real axis would be δ+iε, and the point at which the arc of the cirle intersects the line below the real axis would be δ-iε (though I'm sure other definitions, methods of parameterising the Hankel Contour exist). I suppose it depends upon how analytical you would want to get. ASavantDude (talk) 18:20, 7 March 2018 (UTC)[reply]

All of the information I've found regarding the Hankel contour have explained it was being the two lines connected by the arc of a circle. I added in a bit that explains this process. S. Westaway (talk) 21:14, 27 November 2019 (UTC)[reply]

Hankel Contour Image

The following link contours a (likely poor) image for the Hankel contour. I hope that either (i) this image will be considered for the Hankel contour page OR (ii) It will motivate a better picture by someone else: https://en.wikipedia.org/wiki/File:HankelContour070318_1858.svg

I made an image for the Hankel contour that includes the semicircle arc portion, but if anyone can find/make a better image, then that's all the better. S. Westaway (talk) 21:14, 27 November 2019 (UTC)[reply]

Applications of the Hankel Contour

The article mentions the Gamma Function, but some general indication of the types of contour integral that the Hankel contour will likely be useful for would probably be a good idea (if making good upon this request is possible). I would certainly be interested in knowing why it might not be theoretically possible to associate certain contours with certain Contour Integrals (though I imagine it might not be practically feasible). ASavantDude (talk) 19:21, 7 March 2018 (UTC)[reply]

I found a couple of sources that say that the Hankel contour is used in motivating the Riemann-Zeta function and other Bessel functions of the third kind. S. Westaway (talk) 21:14, 27 November 2019 (UTC)[reply]