# Binomial series

1. Aug 3, 2007

### pivoxa15

1. The problem statement, all variables and given/known data
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.

3. The attempt at a solution
Can't see a way out of it.

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2. Aug 3, 2007

### HallsofIvy

Staff Emeritus
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]
That does not require that $\alpha$ not be a negative integer.

3. Aug 5, 2007

### pivoxa15

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

4. Aug 5, 2007

### Gib Z

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

5. Aug 5, 2007

### pivoxa15

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