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generalized spherical function

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  • Spherical harmonic lighting — Spherical harmonic (SH) lighting is a family of real time rendering techniques that can produce highly realistic shading and shadowing with comparatively little overhead. All SH lighting techniques involve replacing parts of standard lighting… …   Wikipedia

  • Spherical harmonics — In mathematics, the spherical harmonics are the angular portion of an orthogonal set of solutions to Laplace s equation represented in a system of spherical coordinates. Spherical harmonics are important in many theoretical and practical… …   Wikipedia

  • Bessel function — In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel s differential equation: for an arbitrary real or complex number α (the order of the …   Wikipedia

  • Struve function — In mathematics, Struve functions , are solutions y(x) of the non homogenous Bessel s differential equation: introduced by Hermann Struve (1882). The complex number α is the order of the Struve function, and is often an integer. The modified… …   Wikipedia

  • Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia

  • Associated Legendre function — Note: This article describes a very general class of functions. An important subclass of these functions mdash;those with integer ell and m mdash;are commonly called associated Legendre polynomials , even though they are not polynomials when m is …   Wikipedia

  • Spin-weighted spherical harmonics — are generalizations of the standard spherical harmonics and like the usual spherical harmonics are complex functions on the sphere. These harmonics are typically denoted by {} sY {lm}, where s is the spin weight , and l and m are akin to the… …   Wikipedia

  • Harmonic function — In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U rarr; R (where U is an open subset of R n ) which satisfies Laplace s equation,… …   Wikipedia

  • Hypergeometric function of a matrix argument — In mathematics, the hypergeometric function of a matrix argument is a generalization of the classical hypergeometric series. It is the closed form expression of certain multivariate integrals, especially ones appearing in random matrix theory.… …   Wikipedia

  • Gelfand pair — In mathematics, the expression Gelfand pair refers to a pair ( G ,  K ) consisting of a group G and a subgroup K that satisfies a certain property on restricted representations.When G is a finite group the simplest definition is, roughly speaking …   Wikipedia

  • Séminaire Nicolas Bourbaki (1950–1959) — Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s. 1950/51 series *33 Armand Borel, Sous groupes compacts maximaux des groupes de Lie, d après Cartan, Iwasawa et Mostow (maximal compact subgroups) *34 Henri Cartan, Espaces… …   Wikipedia

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