Weierstrass's Elliptic Functions - The Case With 1 A Basic Half-period

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:

    I’m a very smart guy. I haven’t a feeling or a scruple in the world. All I have the itch for is money. I am so money greedy that for twenty-five bucks a day and expenses, mostly gasoline and whisky, I do my thinking myself, what there is of it; I risk my whole future, the hatred of the cops ... I dodge bullets and eat saps, and say thank you very much, if you have any more trouble, I hope you’ll think of me, I’ll just leave one of my cards in case anything comes up.
    Raymond Chandler (1888–1959)

    Southerners, whose ancestors a hundred years ago knew the horrors of a homeland devastated by war, are particularly determined that war shall never come to us again. All Americans understand the basic lessons of history: that we need to be resolute and able to protect ourselves, to prevent threats and domination by others.
    Jimmy Carter (James Earl Carter, Jr.)