# theta1dash

0th

Percentile

##### 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

theta

##### Aliases
• theta1dash
• theta1dashdash
• theta1dashdashdash
##### 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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