gives the value e1 of the Weierstrass elliptic function at the half-period .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- WeierstrassE1 can be evaluated to arbitrary numerical precision.
Examplesopen allclose all
Basic Examples (3)
WeierstrassE1 represents the value of WeierstrassP at its first half-period ω1:
Plot the real and imaginary parts of the e1:
Evaluate to arbitrary precision:
Precision of the output tracks the precision of the input:
Properties & Relations (3)
Values of WeierstrassP at half-periods are the roots of the defining polynomial:
Values of WeierstrassP at half-periods are not linearly independent:
This identity holds for all arguments:
Symmetric polynomials evaluated at values of WeierstrassP at half-periods yield WeierstrassInvariants:
Introduced in 2017