theta1dash {elliptic} | R Documentation |
First, second, and third derivatives of the theta functions
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 |
m as documented in |
q |
q as documented in |
give.n |
Boolean with default |
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
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)