Re: Puzzled by Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg124618] Re: Puzzled by Sum
• From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
• Date: Fri, 27 Jan 2012 06:07:21 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```I am trying to define a function F[X] whose argument is the upper limit in a summation:

A[i_, j_] := i/j + j/i

F[X_] := (Sum[A[i - j, j], {j, 1, i - 1}]) /. i -> X

but when I evaluate, say F[2], I get

-2 DifferenceRoot[{\[FormalY],\[FormalN]}\[Function]{(\[FormalN]-2) \[FormalY](\[FormalN])+(3-2 \[FormalN]) \[FormalY](\[FormalN]+1)+(\[FormalN]-1) \[FormalY](\[FormalN]+2)==0,\[FormalY](0)==0,\[FormalY](1)==-(1/2)}][2]-1

where the result should have been 2:

ii = 2;

Sum[A[ii - j, j], {j, 1, ii - 1}]

2

If I use A[i,j]=i j or other simple functions, everything works as expected.

Themis

Try this:

F[i_] := (Sum[(i - j)/j + j/(i - j), {j, 1, i - 1}]);

F[2]

2

Alexei BOULBITCH, Dr., habil.

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e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu>

```

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