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FunctionExpand—Wolfram Language Documentation

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BUILT-IN SYMBOL

FunctionExpand[expr]

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

Details and Options Examplesopen allclose all 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) Possible Issues  (2)

FunctionExpand may not always expand expressions involving inexact numbers:

Some transformations used by FunctionExpand are only generically valid:

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)

Wolfram Research (1996), FunctionExpand, Wolfram Language function, https://reference.wolfram.com/language/ref/FunctionExpand.html (updated 2008). 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: 12-July-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: 12-July-2025 ]}

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