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modified Bessel functions

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  • 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

  • Bessel-Clifford function — In mathematical analysis, the Bessel Clifford function is an entire function of two complex variables which can be used to provide an alternative development of the theory of Bessel functions. If :pi(x) = frac{1}{Pi(x)} = frac{1}{Gamma(x+1)}is… …   Wikipedia

  • Bessel polynomials — In mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The definition favored by mathematicians is given by the series (Krall Fink, 1948):y n(x)=sum… …   Wikipedia

  • Modified discrete cosine transform — The modified discrete cosine transform (MDCT) is a Fourier related transform based on the type IV discrete cosine transform (DCT IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger… …   Wikipedia

  • Función de Bessel — En matemática, las funciones de Bessel, primero definidas por el matemático Daniel Bernoulli y más tarde generalizadas por Friedrich Bessel, son soluciones canónicas y(x) de la ecuación diferencial de Bessel: (1) donde α es un …   Wikipedia Español

  • Kelvin functions — The Kelvin functions Ber nu;( x ) and Bei nu;( x ) are the real and imaginary parts, respectively, of :J u(x e^{3 pi i/4}),, where x is real, and J u(z), is the nu;th order Bessel function of the first kind. Similarly, the functions Ker nu;( x )… …   Wikipedia

  • List of integrals of exponential functions — The following is a list of integrals (antiderivative functions) of exponential functions. For a complete list of Integral functions, please see the list of integrals. Note that x can be substituted for u, or any other variable, so long as the… …   Wikipedia

  • Meijer G-function — In mathematics, the G function was introduced by Cornelis Simon Meijer (1936) as a very general function intended to include most of the known special functions as particular cases. This was not the only attempt of its kind: the generalized… …   Wikipedia

  • Airy function — This article is about the Airy special function. For the Airy stress function employed in solid mechanics, see Stress functions. In the physical sciences, the Airy function Ai(x) is a special function named after the British astronomer George… …   Wikipedia

  • Cylindrical harmonics — In mathematics, the cylindrical harmonics are a set of linearly independent solutions to Laplace s differential equation, , expressed in cylindrical coordinates, ρ (radial coordinate), φ (polar angle), and z (height). Each function Vn(k) is the… …   Wikipedia

  • Synchrotron radiation — This article concerns the physical phenomenon of synchrotron radiation. For details on the production of this radiation and applications in laboratories, see Synchrotron light source. The electromagnetic radiation emitted when charged particles… …   Wikipedia

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