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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.
• 参见 Mathematica 全书: 3.2.13节.
• 实现注释: 参见 A.9.5节.
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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