O'Reilly logo

The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

III.87 Spherical Harmonics

The starting point for FOURIER ANALYSIS [III.27] is the observation that a wide class of periodic functions f(θ) with period 2π can be decomposed as infinite linear combinations of the TRIGONOMETRIC FUNCTIONS [III.92] sin and cos, or, equivalently, as sums of the form Imageaneinθ.

A useful way to think of a periodic function f defined on the real line is as an equivalent function F defined on Image, the unit circle in the complex plane. A typical point on the circle has the form eiθ, and we define F(eiθ) to be f(θ). (Note that ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required