eta {elliptic}R Documentation

Dedekind's eta function

Description

Dedekind's eta function

Usage

eta(z, ...)
eta.series(z, maxiter=300)

Arguments

z Complex argument
... 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

[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]

Author(s)

Robin K. S. Hankin

References

K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag.

See Also

farey

Examples

 z <- seq(from=1+1i,to=10+0.06i,len=999)
 plot(eta(z))

max(abs(eta(z)-eta.series(z)))

[Package elliptic version 1.2-3 Index]