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function of singularities

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  • Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

  • Harmonic function — In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U rarr; R (where U is an open subset of R n ) which satisfies Laplace s equation,… …   Wikipedia

  • Ackermann function — In recursion theory, the Ackermann function or Ackermann Péter function is a simple example of a general recursive function that is not primitive recursive. General recursive functions are also known as computable functions. The set of primitive… …   Wikipedia

  • Error function — Plot of the error function In mathematics, the error function (also called the Gauss error function) is a special function (non elementary) of sigmoid shape which occurs in probability, statistics and partial differential equations. It is defined …   Wikipedia

  • Meromorphic function — In complex analysis, a meromorphic function on an open subset D of the complex plane is a function that is holomorphic on all D except a set of isolated points, which are poles for the function. (The terminology comes from the Ancient Greek meros …   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

  • Generalized function — In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognised theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going …   Wikipedia

  • Doubly-periodic function — In mathematics, a doubly periodic function is a function f defined at all points z in a plane and having two periods , which are linearly independent vectors u and v such that:f(z) = f(z + u) = f(z + v).,The doubly periodic function is thus a two …   Wikipedia

  • Doubly periodic function — In mathematics, a doubly periodic function is a function defined at all points on the complex plane and having two periods , which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v… …   Wikipedia

  • Mittag-Leffler function — In mathematics, the Mittag Leffler function Eα,β is a special function, a complex function which depends on two complex parameters α and β. It may be defined by the following series when the real part of α is strictly positive: In this case, the… …   Wikipedia

  • Igusa zeta-function — In mathematics, an Igusa zeta function is a type of generating function, counting the number of solutions of an equation, modulo p , p 2, p 3, and so on. Definition For a prime number p let K be a p adic field, i.e. [K: mathbb{Q} p] …   Wikipedia

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