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

Examples

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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:

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)