A Geometric View of Rational Landen Transformations
نویسندگان
چکیده
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
منابع مشابه
A Geometric View of the Rational Landen Transformations
We provide a geometric interpretation of a new rational Landen transformation and establish the convergence of its iterates.
متن کاملRational Landen Transformations on R Dante Manna
The Landen transformation (a, b) → ((a+b)/2, √ ab) preserves the value of an elliptic integral, and its iteration produces the classical arithmeticgeometric mean AGM(a, b). We present analogous transformations for rational functions integrated over the whole real line.
متن کاملRational Landen Transformations on R Dante Manna and Victor
The Landen transformation (a, b) 7→ ((a+b)/2, √ ab) preserves the value of an elliptic integral and its iteration produces the classical arithmeticgeometric mean AGM(a, b). We present analogous transformations for rational functions integrated over the whole real line.
متن کاملLanden transformations and the integration of rational functions
We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm for numerical integration of these functions.
متن کاملSEIMCHA: a new semantic image CAPTCHA using geometric transformations
As protection of web applications are getting more and more important every day, CAPTCHAs are facing booming attention both by users and designers. Nowadays, it is well accepted that using visual concepts enhance security and usability of CAPTCHAs. There exist few major different ideas for designing image CAPTCHAs. Some methods apply a set of modifications such as rotations to the original imag...
متن کامل