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September 4th 2011 | Paperback | PDF, EPUB, FB2, DjVu, AUDIO, mp3, ZIP | 60 pages | ISBN: 9781155645551 | 8.44 Mb

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 59. Chapters: Exponential function, Bessel function, Gamma function, Elliptic integral, Logarithmic integralMorePlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 59. Chapters: Exponential function, Bessel function, Gamma function, Elliptic integral, Logarithmic integral function, Legendre polynomials, Spherical harmonics, Hermite polynomials, Chebyshev polynomials, Laguerre polynomials, Table of spherical harmonics, Error function, Wigner D-matrix, Confluent hypergeometric function, Solid harmonics, Airy function, Exponential integral, Beta function, Bessel polynomials, Fresnel integral, Kelvin functions, Bessel-Clifford function, Trigonometric integral, Gegenbauer polynomials, Jacobi polynomials, Zonal spherical harmonics, Parabolic cylinder function, Cunningham function, Coulomb wave function, Whittaker function, Bateman function, Toronto function.

Excerpt: In mathematics, spherical harmonics are the angular portion of a set of solutions to Laplaces equation. Represented in a system of spherical coordinates, Laplaces spherical harmonics are a specific set of spherical harmonics that forms an orthogonal system, first introduced by Pierre Simon de Laplace. Spherical harmonics are important in many theoretical and practical applications, particularly in the computation of atomic orbital electron configurations, representation of gravitational fields, geoids, and the magnetic fields of planetary bodies and stars, and characterization of the cosmic microwave background radiation.

In 3D computer graphics, spherical harmonics play a special role in a wide variety of topics including indirect lighting (ambient occlusion, global illumination, precomputed radiance transfer, etc.) and recognition of 3D shapes. Spherical harmonics were first investigated in connection with the Newtonian potential of Newtons law of universal gravitation in three dimensions. In 1782, Pierre-Simon de Laplace had, in his M canique C leste, determined that the gravitational potential at a point x associated to a set ...

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