# ck: Coefficients of Laurent expansion of Weierstrass P function In elliptic: Weierstrass and Jacobi Elliptic Functions

## Description

Calculates the coefficients of the Laurent expansion of the Weierstrass P function in terms of the invariants

## Usage

 `1` ```ck(g, n=20) ```

## Arguments

 `g` The invariants: a vector of length two with `g=c(g2,g3)` `n` length of series

## Details

Calculates the series c_k as per equation 18.5.3, p635.

## Author(s)

Robin K. S. Hankin

`P.laurent`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` #Verify 18.5.16, p636: x <- ck(g=c(0.1+1.1i,4-0.63i)) 14*x*x*(389*x^3+369*x^2)/3187041-x #should be zero # Now try a random example by comparing the default (theta function) method # for P(z) with the Laurent expansion: z <- 0.5-0.3i g <- c(1.1-0.2i, 1+0.4i) series <- ck(15,g=g) 1/z^2+sum(series*(z^2)^(0:14)) - P(z,g=g) #should be zero ```

### 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

 2.646978e-23+5.293956e-23i
 2.442491e-15+4.44089e-16i
```

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