ck: Coefficients of Laurent expansion of Weierstrass P function

In RobinHankin/elliptic: Weierstrass and Jacobi Elliptic Functions

Coefficients of Laurent expansion of 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

RobinHankin/elliptic documentation built on Feb. 21, 2024, 6:28 a.m.