convergent infinite product

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• Infinite product — In mathematics, for a sequence of numbers a 1, a 2, a 3, ... the infinite product :prod {n=1}^{infty} a n = a 1 ; a 2 ; a 3 cdotsis defined to be the limit of the partial products a 1 a 2... a n as n increases without bound. The product is said… …   Wikipedia

• Infinite-dimensional holomorphy — In mathematics, infinite dimensional holomorphy is a branch of functional analysis. It is concerned with generalizations of the concept of holomorphic function to functions defined and taking values in complex Banach spaces (or Fréchet spaces… …   Wikipedia

• Euler product — In number theory, an Euler product is an infinite product expansion, indexed by prime numbers p , of a Dirichlet series. The name arose from the case of the Riemann zeta function, where such a product representation was proved by Euler.In general …   Wikipedia

• Cauchy product — In mathematics, the Cauchy product, named after Augustin Louis Cauchy, of two sequences , , is the discrete convolution of the two sequences, the sequence whose general term is given by In other words, it is the sequence whose associated formal… …   Wikipedia

• Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… …   Wikipedia

• Operator product expansion — Contents 1 2D Euclidean quantum field theory 2 General 3 See also 4 External links 2D Euclidean quantum field theory …   Wikipedia

• Blaschke product — In mathematics, the Blaschke product in complex analysis is an analytic function designed to have zeros at a (finite or infinite) sequence of prescribed complex numbers: a 0, a 1, ...inside the unit disc. If the sequence is finite then the… …   Wikipedia

• Continued fraction — Finite continued fraction, where a0 is an integer, any other ai are positive integers, and n is a non negative integer. In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the… …   Wikipedia

• Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

• Riemann zeta function — ζ(s) in the complex plane. The color of a point s encodes the value of ζ(s): dark colors denote values close to zero and hue encodes the value s argument. The white spot at s = 1 is the pole of the zeta function; the black spots on the… …   Wikipedia

• Generalized continued fraction — In analysis, a generalized continued fraction is a generalization of regular continued fractions in canonical form in which the partial numerators and the partial denominators can assume arbitrary real or complex values.A generalized continued… …   Wikipedia