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p-adic series

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  • p-adic exponential function — In mathematics, particularly p adic analysis, the p adic exponential function is a p adic analogue of the usual exponential function on the complex numbers. As in the complex case, it has an inverse function named the p adic logarithm. Contents 1 …   Wikipedia

  • P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

  • p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …   Wikipedia

  • Formal power series — In mathematics, formal power series are devices that make it possible to employ much of the analytical machinery of power series in settings that do not have natural notions of convergence. They are also useful, especially in combinatorics, for… …   Wikipedia

  • p-adic analysis — In mathematics, p adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p adic numbers. The theory of complex valued numerical functions on the p adic numbers is just part of the theory of locally… …   Wikipedia

  • P-adic analysis — In mathematics, p adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p adic numbers.The theory of complex valued numerical functions on the p adic numbers is just part of the theory of locally… …   Wikipedia

  • P-adic quantum mechanics — One may compute the energy levels for a potential well like this one.[note 1] P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p adic analysis to quantum… …   Wikipedia

  • p-adic L-function — In mathematics, a p adic zeta function, or more generally a p adic L function, is a function analogous to the Riemann zeta function, or more general L functions, but whose domain and target are p adic (where p is a prime number). For example, the …   Wikipedia

  • Power series — In mathematics, a power series (in one variable) is an infinite series of the form:f(x) = sum {n=0}^infty a n left( x c ight)^n = a 0 + a 1 (x c)^1 + a 2 (x c)^2 + a 3 (x c)^3 + cdotswhere an represents the coefficient of the n th term, c is a… …   Wikipedia

  • Principal series representation — In mathematics, the principal series representations of certain kinds of topological group G occur in the case where G is not a compact group. There, by analogy with spectral theory, one expects that the regular representation of G will decompose …   Wikipedia

  • Complementary series representation — In mathematics, complementary series representations of a reductive real or p adic Lie groups are certain irreducible unitary representations that are not tempered and do not appear in the decomposition of the regular representation into… …   Wikipedia


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