eta | R Documentation |
Dedekind's \eta
function
eta(z, ...)
eta.series(z, maxiter=300)
z |
Complex argument |
... |
In function |
maxiter |
In function |
Function eta()
uses Euler's formula, viz
\eta(z)=e^{\pi
iz/12}\theta_3\left(\frac{1}{2}+\frac{z}{2},3z\right)
Function eta.series()
is present for validation (and interest)
only; it uses the infinite product formula:
\eta(z)=
e^{\pi iz/12}\prod_{n=1}^\infty\left(1-e^{2\pi inz}\right)
Robin K. S. Hankin
K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag.
farey
z <- seq(from=1+1i,to=10+0.06i,len=999)
plot(eta(z))
max(abs(eta(z)-eta.series(z)))
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