Can x! be Resolved in a Polynomial Form?

[mathelord]

I still think the x! can be resolved 2 a polynomial and then solved normally,or can't it,cos my friend is already working on it and has began to mke progress.
Or can't the x! be resolved let me know

 

[shmoe]

What do you mean "..the x! can be resolved 2 a polynomial and then solved normally.."?

Factorial is only defined on non-negative integers, and not on any real interval (not considering a single point an interval here), so asking about it's integral is a bit of nonsense. Or do you mean factoria'ls usual extension to the Gamma function?

 

[Zurtex]

I still think the x! can be resolved 2 a polynomial and then solved normally,or can't it,cos my friend is already working on it and has began to mke progress.
Or can't the x! be resolved let me know

Almost no functions from Real numbers to Real numbers can be integrated in terms of elementary functions. To my knowledge only polynomials can be integrated to polynomials.

x! is not a function from real numbers to real numbers, it is a function from non-negative integers to non-negative integers and can't be integrated. Even if it could be integrated it grows faster than any polynomial so certainly its integral couldn't even be approximated by a polynomial over its whole domain.

 

[cronxeh]

well great i spend about 2 hours on this problem until i stumbled upon the definition of a Gamma function and Sterling Series
$$n! = \int_{0}^{\infty} e^{-x} x^{n} dx$$

http://mathworld.wolfram.com/StirlingsApproximation.html
http://mathworld.wolfram.com/StirlingsSeries.html

 

[dextercioby]

You could have spelled his name right...

Daniel.