FunctionExpand
 Usage
• FunctionExpand[expr] 试图展开expr中的特殊的和特定的其他函数，可能时化简复合自变量为更简单的自变量。
• FunctionExpand[expr, assum] 使用假设展开。
Notes
• FunctionExpand 使用大的规则集。 • FunctionExpand 应用到一定的三角函数和特殊函数。 • FunctionExpand自动由FullSimplify调用。 • FunctionExpand中的假设可以如同在Simplify中那样指定。 • 例如: FunctionExpand[expr, x  Reals] 假设是一个实数进行展开.
 Further Examples
Here is an elementary simplification.
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The incomplete gamma function with an integer as the first argument can be expressed 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 in which FunctionExpand expresses exotic or specialized functions in terms of more familiar or more fundamental ones.
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Using Assumptions If a, b, c are integers, you can pull out a common factor from GCD.
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This assumes n is an integer greater than  .
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This assumes p and q are distinct primes.
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