spherical harmonics

Together, they make a set of functions called spherical harmonics.

Usually such equations are described by spherical harmonics, but they look very different.

Most commonly, the series is written as a sum of spherical harmonics.

The symbol represents a set of functions known as the spherical harmonics.

In dimensions, the angular variables are Spherical harmonics, for example.

These can be approximated by a sum of spherical harmonics.

The Green function can be expressed in vector spherical harmonics.

Thus, the zonal spherical harmonics can be expressed as follows.

In the mathematical description of atmospheric waves, spherical harmonics are used.

The end of the century also saw a very detailed discussion of spherical harmonics.

He made his way into research mathematics only gradually, becoming an expert in the theory of spherical harmonics.

An efficient method must be used to encode this data, such as spherical harmonics.

Spherical harmonics are often used to approximate the shape of the geoid.

A mathematical result of considerable interest and use is called the "addition theorem" for spherical harmonics.

On the unit sphere, this equivalent to integrating all spherical harmonics up to the same order.

Spherical harmonics are functions that oscillate over the surface of a sphere.

Note that the product of two spherical harmonics can be written in terms of these coefficients.

It follows that the quantities are spherical harmonics, when regarded as a function of x only.

For the sphere, for example, the eigenfunctions are the spherical harmonics.

There exists a more general relationship to the spin-weighted spherical harmonics:

They are, in fact, exactly the zonal spherical harmonics, up to a normalizing constant.

The spherical harmonics turn out to be critical to practical solutions of Laplace's equation.

Radiance can be expanded on a basis set of spherical harmonics .

Robert, A., 1965: The behaviour of planetary waves in an atmospheric model based on spherical harmonics.

In mathematical terms, she has entered an alternate dimension defined by the functions known as spherical harmonics.