elliptic (version 1.5-0)

ck: Coefficients of the Laurent expansion of the Weierstrass P function

Description

Calculates the coefficients of the Laurent expansion of the Weierstrass \(\wp\) function in terms of the invariants

Usage

ck(g, n = 20)

Arguments

g

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

n

length of series

Author

Robin K. S. Hankin

Details

Calculates the series \(c_k\) as per equation 18.5.3, p635.

See Also

P.laurent

Examples

 #Verify 18.5.16, p636:
 x <- ck(g = c(0.1+1.1i, 4-0.63i))
14*x[2]*x[3]*(389*x[2]^3+369*x[3]^2)/3187041-x[11] #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