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

## Description

First, second, and third derivatives of the theta functions

## Usage

 ```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) ```

## Arguments

 `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

## Details

Uses direct expansion as for `theta1()` et seq

## Author(s)

Robin K. S. Hankin

## References

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

`theta`
 ```1 2 3 4 5 6``` ```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) ```