FunctionExpand[expr]
tries to expand out special and certain other functions inexpr, when possible reducing compound arguments to simpler ones.
FunctionExpand[expr,assum]
expands using assumptions.
FunctionExpand
FunctionExpand[expr]
tries to expand out special and certain other functions inexpr, when possible reducing compound arguments to simpler ones.
FunctionExpand[expr,assum]
expands using assumptions.
Details and Options
- FunctionExpand uses a large collection of rules.
- FunctionExpand applies to certain trigonometric functions as well as special functions.
- FunctionExpand attempts to expandDifferentialRoot andDifferenceRoot objects in terms of special and other functions.
- FunctionExpand is automatically called byFullSimplify.
- Assumptions inFunctionExpand can be specified as inSimplify.
- FunctionExpand[expr,x∈Reals] performs expansion assuming thatx is real.
- FunctionExpand has the optionAssumptions, specifying default assumptions to be appended toassum.
- The default setting for theAssumptions option is$Assumptions.
- You can specify default assumptions forFunctionExpand usingAssuming.
- FunctionExpand automatically threads over lists inexpr, as well as equations, inequalities and logic functions.
Examples
open allclose allScope (9)
Expansions of elementary functions and their compositions:
Expansions of orthogonal polynomials and related functions:
FunctionExpand reduces compound arguments to simpler ones:
Expansions of elliptic functions:
Expansions of number theoretic functions:
Expansions of unevaluated derivatives:
Options (3)
Assumptions (3)
Some expansions are valid under additional assumptions:
Heren is assumed to be a generic complex number:
FunctionExpand applies transformations valid for generic indexν:
UseAssumptions to get a specific transformation:
Applications (1)
Rewrite a solution returned byDSolve:
Properties & Relations (2)
The output is generically equivalent to the input:
FunctionExpand is used as a transformation function inFullSimplify:
FullSimplify will produce the simplest form found:
Possible Issues (2)
FunctionExpand may not always expand expressions involving inexact numbers:
Some transformations used byFunctionExpand are only generically valid:
Related Links
Text
Wolfram Research (1996), FunctionExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionExpand.html (updated 2008).
CMS
Wolfram Language. 1996. "FunctionExpand." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008. https://reference.wolfram.com/language/ref/FunctionExpand.html.
APA
Wolfram Language. (1996). FunctionExpand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FunctionExpand.html
BibTeX
@misc{reference.wolfram_2025_functionexpand, author="Wolfram Research", title="{FunctionExpand}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/FunctionExpand.html}", note=[Accessed: 29-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_functionexpand, organization={Wolfram Research}, title={FunctionExpand}, year={2008}, url={https://reference.wolfram.com/language/ref/FunctionExpand.html}, note=[Accessed: 29-November-2025]}
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