Calculating
These harmonics can be explicitly calculated by several methods. The obvious recursion relation results from repeatedly applying the raising or lowering operators. Formulas for direct calculation were derived by Goldberg et al. (1967). Note that their formulas use an old choice for the Condon-Shortley phase. The convention chosen below is in agreement with Mathematica, for instance.
The more useful of the Goldberg, et al., formulas is the following:
A Mathematica notebook using this formula to calculate arbitrary spin-weighted spherical harmonics can be found here.
With the phase convention here and .
Read more about this topic: Spin-weighted Spherical Harmonics
Famous quotes containing the word calculating:
“[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
—Henry Brooks Adams (1838–1918)
“Because relationships are a primary source of self-esteem for girls and women, daughters need to know they will not lose our love if they speak up for what they want to tell us how they feel about things. . . . Teaching girls to make specific requests, rather than being indirect and agreeable, will help them avoid the pitfalls of having to be manipulative and calculating to get what they want.”
—Jeanne Elium (20th century)
“I know that the right kind of leader for the Labour Party is a kind of desiccated calculating machine.”
—Aneurin Bevan (1897–1960)