Laurent series for elliptic and related functions

Laurent series for various functions

P.laurent(z, g=NULL, tol=0, nmax=80)
    Pdash.laurent(z, g=NULL, nmax=80)
    sigma.laurent(z, g=NULL, nmax=8, give.error=FALSE)
sigmadash.laurent(z, g=NULL, nmax=8, give.error=FALSE)
     zeta.laurent(z, g=NULL, nmax=80)

Arguments

z

Primary argument (complex)

g

Vector of length two with g=c(g2,g3)

tol

Tolerance

give.error

In sigma.laurent(), Boolean with default FALSE meaning to return the computed value and TRUE to return the error (as estimated by the sum of the absolute values of the terms along the minor long diagonal of the matrix)

.

nmax

Number of terms used (or, for sigma(), the size of matrix used)

Author

Robin K. S. Hankin

Examples

sigma.laurent(z=1+1i,g=c(0,4))
#> [1] 0.9619402+1.038131i