Neville's form for the theta functions
Neville's notation for theta functions as per section 16.36 of Abramowitz and Stegun.
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", ...)
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
|
Robin K. S. Hankin
M. Abramowitz and I. A. Stegun 1965. Handbook of mathematical functions. New York: Dover
#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.
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