Further Examples: FunctionExpand

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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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 and m and n are positive integers.

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Here are some more examples using assumptions.

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