theta1dash: Derivatives of theta functions
In elliptic: Weierstrass and Jacobi Elliptic Functions

Description Usage Arguments Details Author(s) References See Also Examples

First, second, and third derivatives of the theta functions

1
2
3

theta1dash(z, ignore = NULL, m = NULL, q = NULL, give.n = FALSE, maxiter = 30)
theta1dashdash(z, ignore = NULL, m = NULL, q = NULL, give.n = FALSE, maxiter = 30)
theta1dashdashdash(z, ignore = NULL, m = NULL, q = NULL, give.n = FALSE, maxiter = 30)

`z`	Primary complex argument
`ignore`	Dummy argument to force the user to name the next argument either `m` or `q`
`m`	m as documented in `theta1()`
`q`	q as documented in `theta1()`
`give.n`	Boolean with default `FALSE` meaning to return the function evaluation, and `TRUE` meaning to return a two element list, with first element the function evaluation, and second element the number of iterations used
`maxiter`	Maximum number of iterations

Uses direct expansion as for theta1() et seq

Robin K. S. Hankin

M. Abramowitz and I. A. Stegun 1965. Handbook of Mathematical Functions. New York, Dover

theta

m <- 0.3+0.31i
z <- seq(from=1,to=2+1i,len=7)
delta <- 0.001
deriv.numer <- (theta1dashdash(z=z+delta,m=m) - theta1dashdash(z=z,m=m))/delta
deriv.exact <- theta1dashdashdash(z=z+delta/2,m=m)
abs(deriv.numer-deriv.exact)