Spherical function information

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving...

Spherical function can refer to Spherical harmonics Zonal spherical function This disambiguation page lists mathematics articles associated with the same...

coordinates. Spherical Bessel functions with half-integer α {\displaystyle \alpha } are obtained when solving the Helmholtz equation in spherical coordinates...

In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often...

In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its...

truncation of the incident spherical wave by the lens. In order to measure the point spread function — or impulse response function — of the lens, a perfect...

where φ is a function of a single non-negative real variable. Radial functions are contrasted with spherical functions, and any descent function (e.g., continuous...

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified...

vector fields. The components of the VSH are complex-valued functions expressed in the spherical coordinate basis vectors. Several conventions have been used...

investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly...

traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations...

techniques from analytic function theory (based on complex analysis). The end of the century also saw a very detailed discussion of spherical harmonics. While...

particular fixed axis. The zonal spherical functions are a broad extension of the notion of zonal spherical harmonics to allow for a more general symmetry...

In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i...

standard lighting equations with spherical functions that have been projected into frequency space using the spherical harmonics as a basis. To take a...

uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The...

space of S L ( 2 , R ) {\displaystyle SL(2,\mathbb {R} )} (see Zonal spherical function). Actually the Fourier transform on L 1 ( G / / K ) {\displaystyle...

statistics, a spherical contact distribution function, first contact distribution function, or empty space function is a mathematical function that is defined...

the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known...

equations) in spherical coordinates. Associated Legendre polynomials play a vital role in the definition of spherical harmonics. These functions are denoted...

In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at...

hydrogen atom). It is convenient to use spherical coordinates, and the wave function can be separated into functions of each coordinate, Ψ n ℓ m ( r , θ ...

of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles. The first table of...

summing spherical waves. Let φ(ξ, η, ζ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta function: that...