Jacobi Elliptic Function definition

*To*: mathgroup at smc.vnet.net*Subject*: [mg68340] Jacobi Elliptic Function definition*From*: Roland Franzius <roland.franzius at uos.de>*Date*: Tue, 1 Aug 2006 07:00:18 -0400 (EDT)*Organization*: Universitaet Hannover*Sender*: owner-wri-mathgroup at wolfram.com

The JacobiAmplitude[x,k], JacobiSN[x,k] and related functions are defined in Mathematica by what is not the normal use of the modulus k http://mathworld.wolfram.com/JacobiEllipticFunctions.html Generally ist seems to be the case cn(x,k) = JacobiCN[x,k^2] and so on. E.g the Talor series is Series[JacobiSN[x, k^2], {x, 0, 5}] -> SeriesData[x, 0, {1, 0, -1/6 - k^2/6, 0, 1/120 + (7*k^2)/60 + k^4/120}, 1, 6, 1] and the ODE for sn sn'^2 =(1-sn^2)(1-k^2 sn^2) which is now D[JacobiSN[x, k], x]^2 /. {JacobiCN[x, k]^2 -> 1 - JacobiSN[x, k]^2, JacobiDN[x, k]^2 -> 1 - k*JacobiSN[x, k]^2} results in (1 - JacobiSN[x, k]^2)*(1 - k*JacobiSN[x, k]^2) Does anybody know if this is a feature or a mistake? I don't find any literature using the Mathematica convention. -- Roland Franzius