Special functions

2017-07-27T18:17:58+03:00[Europe/Moscow] en true Polylogarithm, Logistic function, Absolute value, Error function, Gamma function, Sign function, Beta function, Entire function, Exponential integral, Spence's function, Minkowski's question mark function, Closed-form expression, Spin-weighted spherical harmonics, Spin spherical harmonics flashcards Special functions
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  • Polylogarithm
    In mathematics, the polylogarithm (also known as , for Alfred Jonquière) is a special function Lis(z) of order s and argument z.
  • Logistic function
    A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where * e = the natural logarithm base (also known as Euler's number), * x0 = the x-value of the sigmoid's midpoint, * L = the curve's maximum value, and * k = the steepness of the curve.
  • Absolute value
    In mathematics, the absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign.
  • Error function
    In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
  • Gamma function
    In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.
  • Sign function
    In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.
  • Beta function
    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 by Euler and Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital β rather than the similar Latin capital B.
  • Entire function
    In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane.
  • Exponential integral
    In mathematics, the exponential integral Ei is a special function on the complex plane.
  • Spence's function
    In mathematics, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm.
  • Minkowski's question mark function
    In mathematics, the Minkowski question mark function (or the slippery devil's staircase), denoted by ?(x), is a function possessing various unusual fractal properties, defined by Hermann Minkowski (, pages 171–172).
  • Closed-form expression
    In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
  • Spin-weighted spherical harmonics
    In special functions, a topic in mathematics, spin-weighted spherical harmonics are generalizations of the standard spherical harmonics and—like the usual spherical harmonics—are functions on the sphere.
  • Spin spherical harmonics
    In quantum mechanics, spin spherical harmonics Yl, s, j, m are spinors eigenstates of the total angular momentum operator squared: where j = l + s.