Elliptic functions with complex arguments.
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Elliptic functions with complex arguments.

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Published by University of Michigan Press for University of Michigan Research Institute in [Ann Arbor] .
Written in English

Subjects:

  • Elliptic functions.

Book details:

Edition Notes

Bibliography: p. 38.

SeriesUniversity of Michigan Research Institute. Monographs, Monographs (University of Michigan. Research Institute)
Classifications
LC ClassificationsQA343 .H5
The Physical Object
Paginationv, 38 p.
Number of Pages38
ID Numbers
Open LibraryOL5815355M
LC Control Number60063089

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In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a a doubly periodic function cannot be holomorphic, as it would then be a bounded . In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of the electronic elliptic trigonometric functions are defined with reference to a circle, the Jacobi elliptic.   Free kindle book and epub digitized and proofread by Project Gutenberg. Elliptic Functions: An Elementary Text-Book for Students of Mathematics by Baker - Free Ebook Project GutenbergCited by: 2. Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century. The book is divided into four parts. In the first, Lang presents the general analytic theory starting from scratch.

Elliptic functions with complex arguments. ([Ann Arbor] University of Michigan Press for University of Michigan Research Institute, ), by F. M. Henderson (page images at HathiTrust) Elliptic functions: an elementary text-book for students of mathematics / (New York: J. Wiley & Sons, ), by Arthur Latham Baker (page images at HathiTrust). Originally motivated by the computation of the arc length of an ellipse Jacob Jacobi introduced the theory of Jacobi elliptic functions in the book Fundamenta nova theoriae functionum ellipticarum (New foundations of the theory of the elliptic functions) in Jacobi elliptic functions are doubly periodic (in the real and imaginary directions) and meromorphic (analytic with the possible . There is also another development of elliptic functions, due to Weierstrass, which makes essential use of complex variable theory. That approach leads to a set of elliptic functions different from but related to the Jacobi functions. There are other elliptic functions defined as ratios involving sn, cn and dn. a is doubly periodic function in u with periods and, where is the elliptic integral EllipticK. JacobiDN is a meromorphic function in both arguments. For certain special arguments, JacobiDN automatically evaluates to exact values. JacobiDN can be evaluated to arbitrary numerical precision. JacobiDN automatically threads over lists.

1 Introduction In this unit on elliptic functions, we’ll see how two very natural lines of questions interact. The rst, as we have met several times in Berndt’s book, involves ellip-tic integrals. In particular, we seek complex functions which are solutions to the inde nite integral Z dz p Az3 + Bz+ C called an elliptic integral of the rst File Size: KB. The complete elliptic integral associated with EllipticF is EllipticK. EllipticF is the inverse of JacobiAmplitude. If then. EllipticF [ϕ, m] has a branch cut discontinuity running along the ray from to infinity. For certain special arguments, EllipticF automatically evaluates to exact values. EllipticF can be evaluated to arbitrary numerical. If we wish to find the inverse of the elliptic integral x = sinφ = sn(u,k) or u = sn 0 dt! (1− t 2)(1− k2t) While there are 12 different types of Jacobian elliptic functions based on the number of poles and the upper limit on the elliptic integral, the three most popular are the copolar trio of sineFile Size: KB. Elliptic Functions - An Elementary Text-Book for Students of Mathematics - Kindle edition by Baker, Arthur. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Elliptic Functions - An Elementary Text-Book for Students of by: 2.