MathAction #82 Sum should be evaluated by Gosper's method, but isn't

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sum(1/(k*(k+a)), k=1..n) is returned unevaluated

Why doesn't package RationalFunctionSum? handle this?

... --Vladimir Bondarenko, Sun, 30 Jan 2005 07:34:06 -0600 reply

Even worse,

-> sum(1/(k+a), k=1..n)

returns unevaluated while this is obviously

digamma(n+a+1)-digamma(a+1)

... --kratt6, Mon, 31 Jan 2005 11:34:25 -0600 reply

Both sums do not have a hypergeometric solution, it seems to me. I tried Gosper by hand for the first one to find that Gosper fails. Am I mistaken?

Martin

cannot be handled by Gosper --kratt6, Sat, 16 Apr 2005 12:56:21 -0500 reply

Status: open => closed

... --kratt6, Fri, 28 Dec 2007 14:56:15 -0800 reply

Category: Axiom Mathematics => Axiom Library