eta {elliptic} | R Documentation |
Dedekind's eta function
eta(z, ...) eta.series(z, maxiter=300)
z |
Complex argument |
... |
In function eta() , extra arguments sent to
theta3() |
maxiter |
In function eta.series() , maximum value of
iteration |
Function eta()
uses Euler's formula, viz
[omitted; see LaTeX version
Function eta.series()
is present for validation (and interest)
only; it uses the infinite product formula, viz:
[omitted; see LaTeX version]
Robin K. S. Hankin
K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag.
z <- seq(from=1+1i,to=10+0.06i,len=999) plot(eta(z)) max(abs(eta(z)-eta.series(z)))