Everything about Holonomic function
Type of functions, in mathematical analysis
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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Holonomic functionA 5-minute orientation
- Skim a recent paper: Tracking control of chained non‐holonomic systems with asymmetric function constraints and external disturbanceInfluential work since 2022
- Pick up a classic book: Gröbner deformations of hypergeometric differential equationsThe most-reprinted book on the subject
- Read the landmark paper: B-functions and holonomic systemsCited 225 times
- Go sideways: Linear differential equationA closely related topic
- Go sideways: Recurrence relationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
B-functions and holonomic systems
The colored Jones function is q-holonomic
Fast evaluation of holonomic functions
The colored HOMFLYPT function is q-holonomic
On the Non-Holonomic Character of Logarithms, Powers, and the $n$th Prime Function
Holonomic functions in mathematica
On the Holonomic System of $f^s$ and $b$-Function
A strict Lyapunov function for non-holonomic systems under persistently-exciting controllers
🆕 Influential since 2022
Tracking control of chained non‐holonomic systems with asymmetric function constraints and external disturbance
Nonlinear Bayesian filtering via holonomic gradient method with quasi moment generating function
Holonomic functions and prehomogeneous spaces
On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument
Immersion of nonlinear systems comprising holonomic functions
📚 Books worth reading
Gröbner deformations of hypergeometric differential equationsMutsumi Saito, Mutsumi Saito · 2000
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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