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meromorphic functions, that satisfy two periodicity conditions", I suggest "elliptic functions are doubly periodic meromorphic functions", or "elliptic functions are meromorphic functions which are also doubly periodic", etc. In the definition, it can say something like "Elliptic functions are complex functions which are doubly periodic and meromorphic. That is, <insert definitions of doubly periodic and meromorphic: -->
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The article states: "Historically, elliptic functions were first discovered by Carl Gustav Jacobi..." Well, whoever wrote this should definitely read the article "Niels Henrik Abel" by G.Mittag-Leffler( who sure knew what he was talking about!), in which it is proved beyond the shadow of a doubt that
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in the references is eccentric. Better for example to go to
Whittaker & Watson, though their notation is not what the modern standard is (same for all the older books). Tannery and Molk is the classic reference; book by Weber. But the old books are out of print, I suppose - more's the pity.
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For more experienced editors: it seems to me that the description and definition of elliptic functions can be simplified and made more explicit by simply saying that they are (defined as) doubly periodic meromorphic functions. In particular, rather than "elliptic functions are a special kind of
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Different layman question: why is multiplication denoted by a space, instead of using the multiplication symbol or the middle dot (× or · respectively, both listed as common in the wiki article on multiplication)? a' = p·a + q·b in complex analysis context (as opposed to algebraic context) is
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Layman question. Should a' = p a + q b and b' = r a + q b instead read as a' = p a + q b and b' = r a + s b? It seems odd to calculate s and then throw it out. It also seems to leave a degree of freedom, which allows for arbitrary a' and b'.
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Really fundamental in the development of analysis, but the article does not yet reflect this. Only just start in my view, but feel free to adjust the rating and replace this comment.
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the real originator of the theory of elliptic functions is Abel and not Jacobi. Mittag-Leffler's text is available(in French) at the following URL:
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is infinite, but not both, the Cauchy principal value diverges and other means must be used to define the function. If both are infinite, E(
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684:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
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is infinite, the curve is a loop that crosses itself. If both are infinite, the curve is the semicubical parabola
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is wrong I believe, and there are certainly other elliptic functions. I don't know how to rescue this.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Last edited at 21:39, 20 May 2007 (UTC). Substituted at 02:02, 5 May 2016 (UTC)
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article (and the Jacobi & Wierestrass elliptic articles) can reference it.
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that reviews all of the properties of a 2D lattice so that this article and the
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is infinite, the curve consists of one smooth part and one point. If
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semantically clearer and unambiguous. -- Pomax, 8 September 2010
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But I'm not sure how appropriate this is, hence this talk topic.
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Degenerate elliptic functions and curves are obtained by setting
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Simplifying lead and definition: doubly periodic and meromorphic
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elliptic function can also be defined in the same way. Either
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is imaginary (in which case the elliptic curve has one part).
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imaginary (in which case the elliptic curve has two parts, E(
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I just picked up the yellow book. The correct formula is
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741:{\displaystyle f\colon \mathbb {C} \to \mathbb {C} }
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Yes, that is correct, it was a typo in the formula.
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799:Knowledge level-5 vital articles in Mathematics
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