کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9509650 | 1341409 | 2005 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Jacobian elliptic functions as inverses of an integral
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
The 12 Jacobian elliptic functions are traditionally shown as inverses of 12 elliptic integrals, all of them being special cases of â«yx[(a1+b1t2)(a2+b2t2)]-1/2dt in which all quantities are real and either y=0 or x=â or a1+b1y2=0 or a1+b1x2=0. A new unified treatment shows that for each of these four cases the other limit of integration is determined as the inverse function of the integral by the two products a1b2 and a2b1. Inequalities and equalities between these two and 0 distinguish the 12 Jacobian functions, the six circular functions, and the six hyperbolic functions. The proof comes from a corollary of a reduction theorem for the symmetric elliptic integral of the first kind.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 174, Issue 2, 15 February 2005, Pages 355-359
Journal: Journal of Computational and Applied Mathematics - Volume 174, Issue 2, 15 February 2005, Pages 355-359
نویسندگان
B.C. Carlson,