equianharmonic: Special cases of the Weierstrass elliptic function
In elliptic: Weierstrass and Jacobi Elliptic Functions

Description Usage Arguments Details Value Author(s) References See Also Examples

Gives parameters for the equianharmonic case, the lemniscatic case, and the pseudolemniscatic case.

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equianharmonic(...)
lemniscatic(...)
pseudolemniscatic(...)

...

Ignored

These functions return values from section 18.13, p652; 18.14, p658; and 18.15, p662. They use elementary functions (and the gamma function) only, so ought to be more accurate and faster than calling parameters(g=c(1,0)) directly.

Note that the values for the half periods correspond to the general case for complex g2 and g3 so are simple linear combinations of those given in AnS.

One can use parameters("equianharmonic") et seq instead.

Returns a list with the same elements as parameters().

Robin K. S. Hankin

M. Abramowitz and I. A. Stegun 1965. Handbook of Mathematical Functions. New York, Dover.

parameters

P(z=0.1+0.1212i,params=equianharmonic())


x <- seq(from=-10,to=10,len=200)
z <- outer(x,1i*x,"+")
view(x,x,P(z,params=lemniscatic()),real=FALSE)
view(x,x,P(z,params=pseudolemniscatic()),real=FALSE)
view(x,x,P(z,params=equianharmonic()),real=FALSE)