# eta: Dedekind's eta function In elliptic: Weierstrass and Jacobi Elliptic Functions

## Description

Dedekind's eta function

## Usage

 ```1 2``` ```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.

`farey`

## Examples

 ```1 2 3 4``` ``` 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.