In function eta(), extra arguments sent to
theta3()
maxiter
In function eta.series(), maximum value of
iteration
Details
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:
$$\eta(z)=
e^{\pi iz/12}\prod_{n=1}^\infty\left(1-e^{2\pi inz}\right)$$
References
K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag.