About: Holonomic function

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In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory. More precisely, a holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also known as D-finite functions. When a power series in the variables is the Taylor expansion of a holonomic function, the sequence of its coefficients, in one or several indices, is also called holonomic. Holonomic sequences are also called P-recursive sequences: they are defined recursively by multivariate recurrences satisfied b

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rdfs:label	Holonomic function (en)
rdfs:comment	In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory. More precisely, a holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also known as D-finite functions. When a power series in the variables is the Taylor expansion of a holonomic function, the sequence of its coefficients, in one or several indices, is also called holonomic. Holonomic sequences are also called P-recursive sequences: they are defined recursively by multivariate recurrences satisfied b (en)
dcterms:subject	Types of functions Ordinary differential equations Special functions
Wikipage page ID	5817043 (xsd:integer)
Wikipage revision ID	1087207514 (xsd:integer)
Link from a Wikipage to another Wikipage	Bernoulli number Bessel function Binomial coefficient Algebraic function Types of functions Hyperbolic functions D-module Derangement Computer algebra Mathematica Mathematical analysis Mathematics Function of several variables Generalized hypergeometric function Generating function Constant-recursive sequence Holonomic module Linear differential equation Logarithm Closure property Ideal (ring theory) Cauchy product Trigonometric functions Airy function Alternating permutation Error function Exponential function Fibonacci number Field (mathematics) Formal power series Partition (number theory) Differential operator Rational function Recurrence relation Ring (mathematics) Harmonic number Prime number Ordinary differential equations Special functions Characteristic (algebra) Heun function Maple (software) Polynomial Orthogonal polynomials Catalan number Radius of convergence Shift operator Factorial Motzkin number
Link from a Wikipage to an external page	http://perso.ens-lyon.fr/bruno.salvy/%3Fpage_id=48 http://www.risc.jku.at/publications/download/risc_2244/DIPLFORM.pdf http://www.risc.jku.at/research/combinat/software/HolonomicFunctions/ http://kam.mff.cuni.cz/~klazar/irre.pdf http://ddmf.msr-inria.inria.fr http://www.combinatorics.org/Volume_11/Abstracts/v11i2a2.html http://algo.inria.fr/chyzak/mgfun.html http://algo.inria.fr/libraries/
sameAs	Holonomic function Holonomic function Holonomic function Holonomic function
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has abstract	In mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory. More precisely, a holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also known as D-finite functions. When a power series in the variables is the Taylor expansion of a holonomic function, the sequence of its coefficients, in one or several indices, is also called holonomic. Holonomic sequences are also called P-recursive sequences: they are defined recursively by multivariate recurrences satisfied by the whole sequence and by suitable specializations of it. The situation simplifies in the univariate case: any univariate sequence that satisfies a linear homogeneous recurrence relation with polynomial coefficients, or equivalently a linear homogeneous difference equation with polynomial coefficients, is holonomic. (en)
gold:hypernym	Function
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page length (characters) of wiki page	13150 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Holonomic_function
is Link from a Wikipage to another Wikipage of	Enumerations of specific permutation classes Symbolic integration General covariant transformations Christoph Koutschan Constant-recursive sequence

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