Abstract: This paper offers a simple description of the elementary properties of the Jacobian elliptic functions and of the Landen transformation, which connects them with the circular and hyperbolic ...

1 Department of Mathematical and Physical Engineering, College of Engineering Shubra, Benha University, Benha, Egypt. 2 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, ...

We give a survey of elliptic hypergeometric functions associated with root systems, comprised of three main parts. The first two form in essence an annotated table of the main evaluation and ...

IN the preface to his "Elliptic Functions", written in 1892, Prof. A. G. Greenhill complained that, although the subject was then nearly seventy years old, it had not made its way into the ordinary ...

(2 + 1) dimensional Boussinesq and Kadomtsev-Petviashvili equation are investigated by employing Jacobi elliptic function expansion method in this paper. As a result, some new forms traveling wave ...

Abstract: In this paper, we prove a general theta function identity, which contains the quintuple product identity and Winquist’s identity and many other important results of elliptic theta functions ...

We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field ...

I VENTURE to appeal for information as to tables of elliptic functions of the second kind, those by which the lengths of elliptic arcs are evaluated. The best tables accessible to me are those in Dale ...

You’ve probably heard that there are a lot of deep conjectures about L L-functions. For example, there’s the Langlands program. And I guess the Riemann Hypothesis counts too, because the Riemann zeta ...

JacobiElliptic is an implementation of Toshio Fukushima's & Billie C. Carlson's for calculating Elliptic Integrals and Jacobi Elliptic Functions. The default algorithms are set to the Carlson ...