BUILT-IN MATHEMATICA SYMBOL

FunctionExpand

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

FunctionExpand

expands using assumptions.

MORE INFORMATION

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, xReals] 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

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Basic Examples (2)

Expand constants:

Find expansion in terms of simpler functions:

Expand constants:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Find expansion in terms of simpler functions:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

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)

Some expansions are valid under additional assumptions:

Here

is assumed to be a generic complex number:

Assume

to be an integer:

FunctionExpand applies transformations valid for generic index

:

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: