# sn

0th

Percentile

##### Jacobi form of the elliptic functions

Jacobian elliptic functions

Keywords
math
##### 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.

##### References

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

theta

• ss
• sc
• sn
• sd
• cs
• cc
• cn
• cd
• ns
• nc
• nn
• nd
• ds
• dc
• dn
• dd
• e16.36.3
##### Examples
# NOT RUN {
#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)

# }

Documentation reproduced from package elliptic, version 1.4-0, License: GPL-2

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