Holonomic function
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
Christoph KoutschanConstant-recursive sequenceD-finite functionDifferentiably finite functionDifferential equationEnumerations of specific permutation classesFinite functionGeneral covariant transformationsHolonomicHolonomic sequenceIntegralLinear differential equationOrdinary differential equationP-recursive equationRecurrence relationSequenceSymbolic integration
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Holonomic function
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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In mathematics, and more speci ...... al coefficients, is holonomic.
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In mathematics, and more speci ...... ariate recurrences satisfied b
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Holonomic function
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