# theta1dash

From elliptic v1.4-0
by Robin K S Hankin

##### Derivatives of theta functions

First, second, and third derivatives of the theta functions

- Keywords
- math

##### Usage

```
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

##### References

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

##### See Also

##### Examples

```
# NOT RUN {
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)
# }
```

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

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