eta: Dedekind's eta function

In elliptic: Weierstrass and Jacobi Elliptic Functions

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:

[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)))

Example output

Attaching package: 'elliptic'

The following objects are masked from 'package:stats':

    sd, sigma

The following object is masked from 'package:base':

    is.primitive

[1] 1.445008e-14

elliptic documentation built on May 2, 2019, 9:37 a.m.