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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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