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hypergeometric integral

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  • Euler hypergeometric integral — In mathematics, the Euler hypergeometric integral is a representation of the hypergeometric function by means of an integral. It is given by:; 2F 1(a,b;c;z)=frac{Gamma(c)}{Gamma(b) Gamma(c b)}int 0^1 frac{dw} {w^{1 b} ; (1 w)^{1 c+b} ;(1 zw)^a}… …   Wikipedia

  • Hypergeometric — can refer to various related mathematical topics:*Hypergeometric series, p F q , a power series **Confluent hypergeometric function, 1 F 1, also known as the Kummer function **Euler hypergeometric integral, an integral representation of 2 F 1… …   Wikipedia

  • Hypergeometric series — In mathematics, a hypergeometric series is a power series in which the ratios of successive coefficients k is a rational function of k . The series, if convergent, will define a hypergeometric function which may then be defined over a wider… …   Wikipedia

  • Integral — This article is about the concept of integrals in calculus. For the set of numbers, see integer. For other uses, see Integral (disambiguation). A definite integral of a function can be represented as the signed area of the region bounded by its… …   Wikipedia

  • Confluent hypergeometric function — In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular… …   Wikipedia

  • Barnes integral — In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by Ernest William Barnes (1908, 1910). They are closely related to generalized hypergeometric… …   Wikipedia

  • Elliptic integral — In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler. Modern mathematics defines an elliptic integral as any… …   Wikipedia

  • Wallenius' noncentral hypergeometric distribution — Introduction Probability mass function for Wallenius Noncentral Hypergeometric Distribution for different values of the odds ratio ω. m1 = 80, m2 = 60, n = 100, ω = 0.1 ... 20In probability theory and statistics, Wallenius noncentral… …   Wikipedia

  • Selberg integral — In mathematics the Selberg integral is a generalization of Euler beta function to n dimensions introduced and proven by Atle Selberg (1944). Contents 1 Selberg s integral formula 2 Aomoto s integral formula 3 Mehta s integral …   Wikipedia

  • Logarithmic integral function — In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It occurs in problems of physics and has number theoretic significance, occurring in the prime number theorem as an estimate of the number of… …   Wikipedia

  • Trigonometric integral — Si(x) (blue) and Ci(x) (green) plotted on the same plot. In mathematics, the trigonometric integrals are a family of integrals which involve trigonometric functions. A number of the basic trigonometric integrals are discussed at the list of… …   Wikipedia

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