Definition |
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The gamma function is defined by the following integral that shows up frequently in many pure and applied mathematical settings: |
Note that the gamma function with a negative argument is defined by utilizing the recursion formula explained in the next section. |
Important Properties |
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Recursion Formula: Given the following formula, a gamma function at one point can be evaluated recursively in terms of its value at another point: ![]() Generalized Factorial: When x is a positive integer, one can easily prove the following by using the recursive formula: ![]() In fact, many formulas involving n! can be extended to non-integer cases by replacing n! with Reflection Formula: ![]() Multiplication Formula: ![]() |
Some Fractional Values | ||||||||||||
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