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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.
  • FunctionExpand applies to certain trigonometric functions as well as special functions.
  • FunctionExpand automatically threads over lists in expr, as well as equations, inequalities and logic functions.
Expand constants:
Find expansion in terms of simpler functions:
Expand constants:
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Find expansion in terms of simpler functions:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
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:
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:
Rewrite a solution returned by DSolve:
The output is generically equivalent to the input:
FunctionExpand is used as a transformation function in FullSimplify:
FullSimplify will produce the simplest form found:
FunctionExpand may not always expand expressions involving inexact numbers:
Some transformations used by FunctionExpand are only generically valid:
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