sn {elliptic} R Documentation

## Jacobi form of the elliptic functions

### Description

Jacobian elliptic functions

### Usage

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

### Examples


#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)



[Package elliptic version 1.4-0 Index]