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#4753 some limits of gamma toward minf

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open
nobody
limit (170)
5
3 days ago
3 days ago
No

Wrong:

(%i9)   xxx : %e^-x*gamma(-x)*(x+1)^(x+1/2)*sin(%pi*x);
(%o9) %e^-x*gamma(-x)*(x+1)^(x+1/2)*sin(%pi*x)

(%i10)  limit(xxx, x,inf);
(%o10) und

A correct value is

-%e * sqrt(%pi/2)

Negative integers are not in the natural domain of xxx, but xxx does analytically continue to the negative integers.

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