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Legendre function of the first kind

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  • Legendre rational functions — In mathematics the Legendre rational functions are a sequence of functions which are both rational and orthogonal. A rational Legendre function of degree n is defined as::R n(x) = frac{sqrt{2{x+1},L nleft(frac{x 1}{x+1} ight)where L n(x) is a… …   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

  • Gauss–Legendre algorithm — The Gauss–Legendre algorithm is an algorithm to compute the digits of pi;. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of pi;. However, the drawback is that it is memory intensive and it …   Wikipedia

  • Beta function — This article is about Euler beta function. For other uses, see Beta function (disambiguation). In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by for The beta function was studied …   Wikipedia

  • Conical function — In mathematics, conical functions or Mehler functions are functions which can be expressed in terms of Legendre functions of the first and second kind, and The functions were introduced by Gustav Ferdinand Mehler, in 1868, when expanding in… …   Wikipedia

  • Mehler–Fock transform — In mathematics, the Mehler–Fock transform is an integral transform introduced by Mehler (1881) and rediscovered by Fock (1943). It is given by where P is a Legendre function of the first kind. References Brychkov, Yu.A.; Prudnikov, A.P …   Wikipedia

  • Pendulum (mathematics) — The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small angle oscillations. Simple gravity… …   Wikipedia

  • List of letters used in mathematics and science — Some common conventions: * Intensive quantities in physics are usually denoted with minuscules, while extensive are denoted with capital letters. * Most symbols are written in italics. * Vectors are bold. * Sets of numbers are blackboard… …   Wikipedia

  • Heine's identity — In mathematical analysis, Heine s identity, named after Heinrich Eduard Heine [cite book last = Heine first = Heinrich Eduard title = Handbuch der Kugelfunctionen, Theorie und Andwendungen publisher = Physica Verlag date = 1881 place = Wuerzburg… …   Wikipedia

  • Orthogonality — The line segments AB and CD are orthogonal to each other. Orthogonality occurs when two things can vary independently, they are uncorrelated, or they are perpendicular. Contents 1 Mathematics …   Wikipedia

  • Decisional Diffie–Hellman assumption — The decisional Diffie–Hellman (DDH) assumption is a computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the security of many cryptographic protocols, most… …   Wikipedia

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