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 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:
Here n is assumed to be a generic complex number:
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:
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