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1.)how do I find the limit of (x! e^x) / (x^x *x^1/2) as x tends to infinity ?

2.)and is f(x)= x! a function ? if so, how do I find the derivative ?

thanks for any help

Roger

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- Thread starter roger
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1.)how do I find the limit of (x! e^x) / (x^x *x^1/2) as x tends to infinity ?

2.)and is f(x)= x! a function ? if so, how do I find the derivative ?

thanks for any help

Roger

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George Jones

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robert Ihnot said:

I thought about saying this, but then I wondered whether the point of Roger's problem is to derive Stirling's formula.

Regards,

George

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George Jones

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Regards,

George

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thanks for your help

Can I find the limit without using sterlings formula ?

Can I find the limit without using sterlings formula ?

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When I learned about Sterling's formula it was a graduate course and the professor put the derivation on the board. It is not that simple. Note the presence of [tex]\sqrt(2n\pi)[/tex]. This frquently means the use of complex integration, but not here: http://courses.ncssm.edu/math/Stat_Inst/PDFS/appndx_1.pdf

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interesting formula

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George Jones said:

Regards,

George

Thanks for the information.

Does the extension to real numbers excluding negative, mean that the factorial becomes 'continuous' so that a derivative exists ?

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Yes and its usually expressed in terms of digamma function.roger said:Does the extension to real numbers excluding negative, mean that the factorial becomes 'continuous' so that a derivative exists ?

-- AI

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