Elljac

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Elliptic functions

Elljac functions as per the Gnu Scientific Library, reference manual section 7.14 and AMS-55, chapter 16. These functions are declared in header file gsl_sf_elljac.h

Keywords
array
Usage
elljac(u, m, give=FALSE, strict=TRUE)
sn(z,m)
cn(z,m)
dn(z,m)
ns(z,m)
nc(z,m)
nd(z,m)
sc(z,m)
sd(z,m)
cs(z,m)
cd(z,m)
ds(z,m)
dc(z,m)
Arguments
u,m
input: real values
z
input: complex values
give
Boolean with TRUE meaning to return a list of three items: the value, an estimate of the error, and a status number
strict
Boolean, with TRUE meaning to return NaN if status is an error
Details

A straightforward wrapper for the gsl_sf_elljac_e function of the GSL library, except for sn(), cn(), and dn(), which implement 16.21.1 to 16.21.4 (thus taking complex arguments); and ns() et seq which are the minor elliptic functions.

References

http://www.gnu.org/software/gsl

Aliases
  • Elljac
  • elljac
  • sn
  • cn
  • dn
  • ns
  • nc
  • nd
  • sc
  • sd
  • cs
  • cd
  • ds
  • dc
Examples
K <- ellint_F(phi=pi/2,k=sqrt(1/2))  #note the sqrt: m=k^2
u <- seq(from=0,to=4*K,by=K/24)
jj <- elljac(u,1/2)
plot(u,jj$sn,type="l",xaxt="n",yaxt="n",bty="n",ylab="",xlab="",main="Fig 16.1, p570")
lines(u,jj$cn,lty=2)
lines(u,jj$dn,lty=3)
axis(1,pos=0,at=c(K,2*K,3*K,4*K),labels=c("K","2K","3K","4K"))
abline(0,0)
axis(2,pos=0,at=c(-1,1))
text(1.8*K,0.6,"sn u")
text(1.6*K,-0.5,"cn u")
text(2.6*K,0.9,"dn u")



 a <- seq(from=-5,to=5,len=100)
jj <- outer(a,a,function(a,b){a})
z <- jj+1i*t(jj)
e <- Re(cd(z,m=0.2))
e[abs(e)>10] <- NA
contour(a,a,e,nlev=55)
Documentation reproduced from package gsl, version 1.9-2, License: GPL-2

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