gives the holonomic function , specified by the linear differential equation lde[h,x].
represents a pure holonomic function .
- Mathematical function, suitable for both symbolic and numerical manipulation; also known as holonomic function and D-finite function.
- The holonomic function defined by a DifferentialRoot function satisfies a holonomic differential equation with polynomial coefficients and initial values .
- DifferentialRoot can be used like any other mathematical function.
- FunctionExpand will attempt to convert DifferentialRoot functions in terms of special functions.
- The functions representable by DifferentialRoot include a large number of special functions.
- DifferentialRootReduce can convert most special functions to DifferentialRoot functions.
- Holonomic functions are closed under many operations, including:
constant multiple, integer power sums and products composition with polynomial, rational, and algebraic functions convolution derivatives and integrals
- DifferentialRoot is automatically generated by functions such as Integrate, DSolve, and GeneratingFunction.
- Functions such as Integrate, D, SeriesCoefficient, and DSolve work with DifferentialRoot inputs.
- DifferentialRoot can be evaluated to arbitrary numerical precision.
- DifferentialRoot automatically threads over lists.
- DifferentialRoot[lde,pred] represents a solution restricted to avoid cuts in the complex plane defined by pred[z], where pred[z] can contain equations and inequalities.
Examplesopen allclose all
Basic Examples (2)
Generalizations & Extensions (1)
Find the DifferentialRoot object of a special function:
Introduced in 2008