theta.neville

0th

Percentile

Neville's form for the theta functions

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

Keywords
math
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

References

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

Aliases
• theta.neville
• theta.s
• theta.c
• theta.d
• theta.n
• e16.36.6
• e16.36.6a
• e16.36.6b
• e16.36.7
• e16.36.7a
• e16.36.7b
• e16.37.1
• e16.37.2
• e16.37.3
• e16.37.4
• e16.38.1
• e16.38.2
• e16.38.3
• e16.38.4
Examples
# NOT RUN {
#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.

# }

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

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