On extremal properties of Jacobian elliptic functions with complex modulus

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fast Computation of Complete Elliptic Integrals and Jacobian Elliptic Functions

As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9 to 19 obtained by truncating Taylor series exp...

متن کامل

Power series for inverse Jacobian elliptic functions

The 12 inverse Jacobian elliptic functions are expanded in power series by using properties of the symmetric elliptic integral of the first kind. Suitable notation allows three series to include all 12 cases, three of which have been given previously. All coefficients are polynomials in the modulus k that are homogeneous variants of Legendre polynomials. The four series in each of three subsets...

متن کامل

Inequalities for Jacobian elliptic functions and Gauss lemniscate functions

A new proof of inequalities involving Jacobian elliptic functions and their inverse functions are obtained. Similar results for the Gauss lemniscate functions are also established. Upper bounds for the inverse Jacobian elliptic functions and for the Gauss arc lemniscate functions are derived. 2012 Elsevier Inc. All rights reserved.

متن کامل

Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves

Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...

متن کامل

Extremal Properties of Complex Networks

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Mathematical Analysis and Applications

سال: 2016

ISSN: 0022-247X

DOI: 10.1016/j.jmaa.2016.05.008