# sn: Jacobi form of the elliptic functions In elliptic: Weierstrass and Jacobi Elliptic Functions

## Description

Jacobian elliptic functions

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```ss(u,m, ...) sc(u,m, ...) sn(u,m, ...) sd(u,m, ...) cs(u,m, ...) cc(u,m, ...) cn(u,m, ...) cd(u,m, ...) ns(u,m, ...) nc(u,m, ...) nn(u,m, ...) nd(u,m, ...) ds(u,m, ...) dc(u,m, ...) dn(u,m, ...) dd(u,m, ...) ```

## Arguments

 `u` Complex argument `m` Parameter `...` Extra arguments, such as `maxiter`, passed to `theta.?()`

## Details

All sixteen Jacobi elliptic functions.

## Author(s)

Robin K. S. Hankin

## References

M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover

`theta`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46``` ```#Example 1, p579: nc(1.9965,m=0.64) # (some problem here) # Example 2, p579: dn(0.20,0.19) # Example 3, p579: dn(0.2,0.81) # Example 4, p580: cn(0.2,0.81) # Example 5, p580: dc(0.672,0.36) # Example 6, p580: Theta(0.6,m=0.36) # Example 7, p581: cs(0.53601,0.09) # Example 8, p581: sn(0.61802,0.5) #Example 9, p581: sn(0.61802,m=0.5) #Example 11, p581: cs(0.99391,m=0.5) # (should be 0.75 exactly) #and now a pretty picture: n <- 300 K <- K.fun(1/2) f <- function(z){1i*log((z-1.7+3i)*(z-1.7-3i)/(z+1-0.3i)/(z+1+0.3i))} # f <- function(z){log((z-1.7+3i)/(z+1.7+3i)*(z+1-0.3i)/(z-1-0.3i))} x <- seq(from=-K,to=K,len=n) y <- seq(from=0,to=K,len=n) z <- outer(x,1i*y,"+") view(x, y, f(sn(z,m=1/2)), nlevels=44, imag.contour=TRUE, real.cont=TRUE, code=1, drawlabels=FALSE, main="Potential flow in a rectangle",axes=FALSE,xlab="",ylab="") rect(-K,0,K,K,lwd=3) ```