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#4759 limits of gamma toward a negative integer

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open
nobody
5
1 day ago
1 day ago
No

Wrong--when n is a negative integer, this limit is undefined:

(%i1)   declare(n,integer);
(%o1)   done

(%i2)   limit(gamma(x),x,n);
(%o2)   (n-1)!

Let's assume n is negative:

(%i3)   assume(n < 0);
(%o3)   [n<0]

(%i4)   limit(gamma(x),x,n,plus);
(%o4)   inf

No, Maxima needs to ask if n is even or odd--consider:

(%i5)   limit(gamma(x),x,-5,plus);
(%o5)   minf

(%i6)   limit(gamma(x),x,-5, minus);
(%o6)   inf

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