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FunctionExpand
FunctionExpand[
expr
] tries to expand out special functions in expr, when possible reducing compound arguments to simpler ones.
FunctionExpand uses a large collection of rules.
FunctionExpand is automatically called by FullSimplify.
See the Mathematica book: Section 3.2.13.
See also: TrigExpand, TrigToExp, ComplexExpand, FullSimplify.
Further Examples
Here is an elementary simplification.
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The incomplete gamma function with an integer as the first argument is expressible in terms of exponentials.
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The next few examples yield results that still contain special functions, but are considered simpler by Mathematica because the arguments of the resulting special functions are simpler.
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FunctionExpand acts like PowerExpand when appropriate.
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Here FunctionExpand refrains from distributing the exponent, since  and  are not always equal.
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A common use of FunctionExpand is to simplify trigonometric expressions involving integer or half-integer multiples of the arc.
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Many functions can be expressed in terms of gamma functions.
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This can be convenient in checking identities.
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Here are some other examples where FunctionExpand expresses exotic or specialized functions in terms of more familiar or more fundamental ones.
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THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. | | | |
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