FunctionExpand [expr]
tries to expand out special and certain other functions in expr, 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 in expr, 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 expand DifferentialRoot and DifferenceRoot objects in terms of special and other functions.
- FunctionExpand is automatically called by FullSimplify .
- Assumptions in FunctionExpand can be specified as in Simplify .
- FunctionExpand [expr,x∈Reals ] performs expansion assuming that x is real.
- FunctionExpand has the option Assumptions , specifying default assumptions to be appended to assum.
- The default setting for the Assumptions option is $Assumptions .
- You can specify default assumptions for FunctionExpand using Assuming .
- FunctionExpand automatically threads over lists in expr, as well as equations, inequalities and logic functions.
Examples
open all close allBasic Examples (2)
Expand constants:
Find expansion in terms of simpler functions:
Scope (9)
Expansions of constants:
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:
Expansions of hypergeometric family functions:
Expansion of special functions:
Options (3)
Assumptions (3)
Some expansions are valid under additional assumptions:
Here n is assumed to be a generic complex number:
Assume n to be an integer:
FunctionExpand applies transformations valid for generic index ν:
Use Assumptions to get a specific transformation:
Applications (1)
Rewrite a solution returned by DSolve :
Properties & Relations (2)
The output is generically equivalent to the input:
FunctionExpand is used as a transformation function in FullSimplify :
FullSimplify will produce the simplest form found:
Possible Issues (2)
FunctionExpand may not always expand expressions involving inexact numbers:
Some transformations used by FunctionExpand are only generically valid:
Related Links
History
Introduced in 1996 (3.0) | Updated in 1999 (4.0) ▪ 2000 (4.1) ▪ 2002 (4.2) ▪ 2003 (5.0) ▪ 2007 (6.0) ▪ 2008 (7.0)
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: 24-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: 24-November-2025]}