The Case With 1 A Basic Half-period
If, much of the above theory becomes simpler; it is then conventional to write for . For a fixed τ in the upper half-plane, so that the imaginary part of τ is positive, we define the Weierstrass ℘ function by
The sum extends over the lattice {n+mτ : n and m in Z} with the origin omitted. Here we regard τ as fixed and ℘ as a function of z; fixing z and letting τ vary leads into the area of elliptic modular functions.
Read more about this topic: Weierstrass's Elliptic Functions
Famous quotes containing the words case and/or basic:
“He was then in his fifty-fourth year, when even in the case of poets reason and passion begin to discuss a peace treaty and usually conclude it not very long afterwards.”
—G.C. (Georg Christoph)
“Of course I lie to people. But I lie altruistically—for our mutual good. The lie is the basic building block of good manners. That may seem mildly shocking to a moralist—but then what isn’t?”
—Quentin Crisp (b. 1908)