| 1. | Examples of such functions include the factorial function and related functions.
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| 2. | For instance, the factorial function can be expressed as:
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| 3. | The second one is based on analytic bounds for the factorial function.
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| 4. | So the function given by is an extension of the factorial function.
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| 5. | Besides elementary arithmetic only the factorial function and the power function is employed.
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| 6. | XEQ FACT for the factorial function.
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| 7. | Also, the factorial function talk ) 22 : 39, 15 July 2008 ( UTC)
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| 8. | As an example, the factorial function is defined on the nonnegative integers and produces a nonnegative integer.
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| 9. | For example, the factorial function can be defined recursively by the equations and, for all,.
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| 10. | Alternatively, this can be taken as an extension of the q-factorial function to the real number system.
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