Special cases of the Weierstrass elliptic function
Gives parameters for the equianharmonic case, the lemniscatic case, and the pseudolemniscatic case.
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.
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)
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