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BUILT-IN MATHEMATICA SYMBOL
DifferentialRoot
DifferentialRoot[lde]
represents a function that solves the linear differential equation specified by 
.
Details
- DifferentialRoot is also known as a holonomic function or D-finite function.
- DifferentialRoot works like Function.
- DifferentialRoot[lde][s] finds the value of the solution to the differential equation at the specific point s.
- DifferentialRoot[lde] essentially gives a representation of the solution for y in DSolve[lde[y, x], y, x].
- DifferentialRoot is generated by functions such as Integrate, DSolve, and GeneratingFunction.
- Functions such as Integrate, D, and Series can be used on DifferentialRoot objects.
- DifferentialRoot[lde][{s1, s2, ...}], etc. threads automatically over lists.
- DifferentialRootReduce can be used to reduce combinations of DifferentialRoot objects and other functions to a single DifferentialRoot object.
- FunctionExpand will attempt to expand DifferentialRoot objects in terms of ordinary special and elementary functions.
- DifferentialRoot[lde, pred] represents a solution restricted to avoid cuts in the complex
plane defined by 
, where 
can contain equations and inequalities.
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