Timeline for Looking for modern reference for asymptotic of Barnes integral
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2016 at 11:08 | comment | added | Lev Borisov | Great, thank you! I have not looked at these. | |
| Oct 27, 2016 at 8:02 | comment | added | M.G. | Have you already looked in the book "Asymptotic Expansions of Integrals" of Bleistein and Handelsman? Its reprint is from 1975, so maybe not that modern, but I have a vague memory that it treated some Barnes integrals. BTW, have you also looked in Paris and Kaminski's "Asymptotics and Mellin-Barnes Integrals" (2001)? | |
| Oct 27, 2016 at 1:33 | comment | added | Lev Borisov | Thank you, I will take a look at it. I saw that reference in Luke's book. Was under the impression that the idea was to approximate $\Gamma(s)^N$ by $\Gamma(Ns-i)$, will look in more detail. | |
| Oct 27, 2016 at 1:30 | comment | added | post.as.a.guest | Look at Braaksma in Compositio 1963. eudml.org/doc/88877 This is what Luke cites for instance. The sketch in Section 2.2, with some bits from Section 3 involving $\Gamma$-expansions, is already probably enough for the ideas. Much of the 100 pages is chasing down uniformity IIRC. Historically, I think that Stokes might have actually have obtained the asymptotic term, and Barnes the error (or an expansion), but I must admit parsing Barnes was hard when I tried | |
| Oct 27, 2016 at 1:18 | history | asked | Lev Borisov | CC BY-SA 3.0 |