P-function | Weierstrass P-function

The Weierstrass elliptic functions (or Weierstrass ℘-functions, voiced "p-functions") are elliptic functions which, unlike the Jacobi elliptic functions, have a second-order pole at z = 0. To specify ℘(z) completely, its half-periods (ω_1 and ω_2) or elliptic invariants (g_2 and g_3) must be specified. These two cases are denoted ℘(z|ω_1, ω_2) and ℘(z;g_2, g_3), respectively.

Eisenstein series | elliptic curve | elliptic function | elliptic invariants | equianharmonic case | half-period | half-period ratio | Jacobi elliptic functions | lemniscate case | ω_2 constant | pseudolemniscate case | Weierstrass sigma function | Weierstrass zeta function

Karl Weierstrass