Timeline for Errata for Emil Artin's 'The Gamma Function'?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| May 9, 2010 at 14:11 | comment | added | Jim Humphreys | P.S. At the moment the AMS book mentioned earlier is on sale online: Exposition by Emil Artin: A Selection - Michael Rosen, Brown University, Editor - AMS | LMS, 2006, 346 pp., Softcover, ISBN-10: 0-8218-4172-6, ISBN-13: 978-0-8218-4172-3, List: US$59, All AMS Members: US$47, Sale Price: US$38, HMATH/30 | |
| Apr 4, 2010 at 18:10 | vote | accept | Zavosh | ||
| Apr 4, 2010 at 17:29 | comment | added | Jim Humphreys |
Since this section of Artin's book is concerned with approximating the gamma function, there may be some tendency to use the equals sign loosely. I guess the point is to find a convenient elementary function giving a good approximation for large $x$; the choice might be fine-tuned in various ways. But in the era before computers the shape of an approximating function would have been the most interesting question for many people.
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| Apr 4, 2010 at 16:38 | comment | added | Zavosh | I looked at the AMS 2007 version and it's exactly the same. I will mark your answer as accepted soon, unless someone else comes up with a miraculously clarifying answer (which is unlikely.) Thanks very much. | |
| Apr 4, 2010 at 16:35 | comment | added | Zavosh | I think $\theta$ actually converges to 1 quickly as $x$ grows large. For just an asymptotic formula for $\Gamma(x)$ (as in the common version of Stirling's formula), there would be no reason to mention $\mu(x)$ or $\theta$ at all, since the $e^{-\mu(x)}$ term converges to 1. It sounds like the author is stating on page 24 an exact formula involving a constant $\theta$, when it's actually not a constant. I suspect it's a mistake of the translator originating from a misunderstanding on page 22. | |
| Apr 4, 2010 at 15:54 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
added 165 characters in body; edited body
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| Apr 4, 2010 at 14:16 | history | answered | Jim Humphreys | CC BY-SA 2.5 |