theta.neville {elliptic}

Neville's form for the theta functions

Description

Neville's notation for theta functions as per section 16.36 of Abramowitz and Stegun.

Usage

theta.s(u, m, method = "16.36.6", ...)
theta.c(u, m, method = "16.36.6", ...)
theta.d(u, m, method = "16.36.7", ...)
theta.n(u, m, method = "16.36.7", ...)

Arguments

u

Primary complex argument

m

Real parameter

method

Character string corresponding to A and S's equation numbering scheme

...

Extra arguments passed to the method function, such as maxiter

Author(s)

Robin K. S. Hankin

References

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

Examples

#Figure 16.4.
m <- 0.5
K <- K.fun(m)
Kdash <- K.fun(1-m)
x <- seq(from=0,to=4*K,len=100)
plot  (x/K,theta.s(x,m=m),type="l",lty=1,main="Figure 16.4, p578")
points(x/K,theta.n(x,m=m),type="l",lty=2)
points(x/K,theta.c(x,m=m),type="l",lty=3)
points(x/K,theta.d(x,m=m),type="l",lty=4)
abline(0,0)



#plot a graph of something that should be zero:
 x <- seq(from=-4,to=4,len=55)
 plot(x,(e16.37.1(x,0.5)-theta.s(x,0.5)),pch="+",main="error: note vertical scale")

#now table 16.1 on page 582 et seq:
 alpha <- 85
 m <- sin(alpha*pi/180)^2
## K <- ellint_Kcomp(sqrt(m))
 K <- K.fun(m)
 u <- K/90*5*(0:18)
 u.deg <- round(u/K*90)
 cbind(u.deg,"85"=theta.s(u,m))      # p582, last col. 
 cbind(u.deg,"85"=theta.n(u,m))      # p583, last col.