theta1dash {elliptic} R Documentation

## Derivatives of theta functions

### Description

First, second, and third derivatives of the theta functions

### 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

### Author(s)

Robin K. S. Hankin

### References

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

theta

### Examples

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)



[Package elliptic version 1.4-0 Index]