Campus Livre
ellipticNome
Elliptic nome q for a given parameter.
Category: Mathematics > Mathematical Functions
Syntax
q = ellipticNome(m)Returns exp(-pi*ellipticCK(m)/ellipticK(m)).
Description
The nome is the variable of the q-series of theta functions and of the elliptic functions. It is small even for sizeable m: for m = 0.5 it is about 0.0432, which is why q-series converge so quickly. It rises monotonically from 0 at m = 0 to 1 as m approaches 1.
Input arguments
m- Parameter,
0 <= m < 1for real values.
Output arguments
q- Nome, between 0 and 1 for real
m.
Example
Nome from its definition
m = 0.5;
q = ellipticNome(m)
exp(-pi*ellipticCK(m)/ellipticK(m))Output
q = 0.0432
ans = 0.0432