کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4668147 1345499 2007 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An addition formula for the Jacobian theta function and its applications
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
An addition formula for the Jacobian theta function and its applications
چکیده انگلیسی

In this paper, we prove an addition formula for the Jacobian theta function using the theory of elliptic functions. It turns out to be a fundamental identity in the theory of theta functions and elliptic function, and unifies many important results about theta functions and elliptic functions. From this identity we can derive the Ramanujan cubic theta function identity, Winquist's identity, a theta function identities with five parameters, and many other interesting theta function identities; and all of which are as striking as Winquist's identity. This identity allows us to give a new proof of the addition formula for the Weierstrass sigma function. A new identity about the Ramanujan cubic elliptic function is given. The proofs are self contained and elementary.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 212, Issue 1, 20 June 2007, Pages 389-406