Equation with Negative Alpha Causes Problem

[pivoxa15]

Homework Statement

The equation is in the document
If alpha was negative like -3 then you have gamma(-3+1)=gamma(-2) which is not allowed.
Looks like alpha can be negative in the equation. So there looks like a problem.

The Attempt at a Solution

Can't see a way out of it.

 

[HallsofIvy]

Then use the other definition given in the problem:
[tex]\left(\begin{array}{c}\alpha\\ k\end{array}\right)= \frac{\alpha (\alpha -1)(\alpha- 2)\cdot\cdot\cdot(\alpha- k+1)}{k!}[/itex]<br /> That does not require that $\alpha$ not be a negative integer.[/tex]

 

[pivoxa15]

Isn't that inconsistent? They are an equality. Or is it the weird case that when alpha is -3 then the combined gamma functions produce a valid result?

 

[Gib Z]

Well note the attachment says alpha and x are elements in the Reals, it didn't state positive. Perhaps there's something weird about this textbook..

 

[pivoxa15]

It appeared in an exam formula sheet. So its quite serious.