tries to expand out special and certain other functions in expr, when possible reducing compound arguments to simpler ones.


expands using assumptions.

Details and Options


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Basic 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:

Wolfram Research (1996), FunctionExpand, Wolfram Language function, (updated 2008).


Wolfram Research (1996), FunctionExpand, Wolfram Language function, (updated 2008).


Wolfram Language. 1996. "FunctionExpand." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2008.


Wolfram Language. (1996). FunctionExpand. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2021_functionexpand, author="Wolfram Research", title="{FunctionExpand}", year="2008", howpublished="\url{}", note=[Accessed: 24-January-2022 ]}


@online{reference.wolfram_2021_functionexpand, organization={Wolfram Research}, title={FunctionExpand}, year={2008}, url={}, note=[Accessed: 24-January-2022 ]}