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

In elliptic: Weierstrass and Jacobi Elliptic Functions

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

Details

Calculates the series c_k as per equation 18.5.3, p635.

Author(s)

Robin K. S. Hankin

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

elliptic documentation built on Nov. 11, 2025, 1:07 a.m.