[Maxima-bugs] [ maxima-Bugs-831354 ] beta(-2,1) inconsistent

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Bugs item #831354, was opened at 2003-10-27 16:45
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Submitted By: Stavros Macrakis (macrakis)
Assigned to: Nobody/Anonymous (nobody)
Summary: beta(-2,1) inconsistent

Initial Comment:
beta(-2,    1) => -1/2
beta(-2.0, 1) => -0.5

BUT

beta(-2.0, 1.0) => -0.25

The fundamental problem is that beta(x,y) is undefined 
as a continuous real function of both x and y at (-2,1), 
but that beta(x,1) can be extended to be a well-
behaved continuous function of x, namely 1/x.

This is essentially the same case as x^y at (0,0).  Right 
now, Maxima simplifies x^0=>1 and 0^x=>0 (just like 
beta(x,1)).  The difference is that Maxima gives an error 
for 0^0, 0.0^0, etc.

Longer-term, it would be nice if 0^x kept as a side-
condition (x # 0) of the simplification, but for now....


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