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:
“It is almost everywhere the case that soon after it is begotten the greater part of human wisdom is laid to rest in repositories.”
—G.C. (Georg Christoph)
“Insecurity, commonly regarded as a weakness in normal people, is the basic tool of the actor’s trade.”
—Miranda Richardson (b. 1958)