Equation with Negative Alpha Causes Problem

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Homework Help Overview

The discussion revolves around an equation involving the gamma function and the parameter alpha, specifically addressing the implications of alpha being negative. Participants are exploring the constraints and definitions related to the gamma function in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants question the validity of using a negative alpha in the equation, particularly in relation to the gamma function. Others suggest considering an alternative definition that accommodates negative integers.

Discussion Status

The discussion is ongoing, with participants examining different interpretations of the definitions provided in the problem. There is a recognition of potential inconsistencies, and some guidance has been offered regarding alternative formulations that may resolve the issue.

Contextual Notes

Participants note that the problem states alpha and x are elements of the reals, without specifying positivity, which raises questions about the assumptions made in the textbook and the implications for the equation.

pivoxa15
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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.
 

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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]<br /> That does not require that [itex]\alpha[/itex] not be a negative integer.[/tex]
 
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?
 
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..
 
It appeared in an exam formula sheet. So its quite serious.
 

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