On functions of Jacobi-Weierstrass (I) and equation of Painleve
Abstract
Description
The paper is an essentially extended version of the work math.CA/0601371, supplemented with an application. We present new results in the theory of classical $θ$-functions of Jacobi and $σ$-functions of Weierstrass: ordinary differential equations and series expansions. We also give the extension of canonical $θ$-functions and consider an application to the sixth Painlevé equation (P6). Picard--Hitchin's general solution of P6 is represented explicitly in a form of logarithmic derivative of a corresponding $τ$-function (Painlevé's form).
In Russian; 33 pages; 1 figure
In Russian; 33 pages; 1 figure