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Binomial series

  1. Aug 3, 2007 #1
    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.
     

    Attached Files:

  2. jcsd
  3. Aug 3, 2007 #2

    HallsofIvy

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    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 [itex]\alpha[/itex] not be a negative integer.
     
  4. Aug 5, 2007 #3
    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?
     
  5. Aug 5, 2007 #4

    Gib Z

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    Homework Helper

    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..
     
  6. Aug 5, 2007 #5
    It appeared in an exam formula sheet. So its quite serious.
     
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