sn: Jacobi form of the elliptic functions

In RobinHankin/elliptic: Weierstrass and Jacobi Elliptic Functions

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

See Also

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)

RobinHankin/elliptic documentation built on Feb. 21, 2024, 6:28 a.m.