Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence

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8
votes
3answers
1k views

Ways to compute inner products of tensors

One way to evaluate the following sums is combining Table and Sum: $u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$ $q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$ It will look like ...
4
votes
2answers
248 views

What causes this strange convergent sum?

N[Sum[1/(x^2 + 1), {x, 1, Infinity}], 5] N[Sum[1/(x^2 + x + 1), {x, 1, Infinity}], 5] 1.0767 0.79815 + 0.*10^-6 I What causes the strange number?
2
votes
1answer
445 views

Mathematica 9 behavior with derivative of a sum

In: D[Sum[Sin[x],x],x] D[Sum[f[x],x],x] Out: 1/2 Cos[1/2 (-1 - Pi + 2 x)] Csc[1/2] 0 Function f is undefined, but Mathematica 9 counts it as constant? ...
16
votes
4answers
2k views

how to differentiate formally?

I have been wrapping my head around this for a while now and I have not found a solution so far. I want to work with an arbitrary number of variables in mathematica and use some built in functions. ...
17
votes
2answers
1k views

Sum or Product with Exclusions

Is there a built-in feature for handling things like: $$\sum_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ and $$\prod_{\substack{i=0\\i\ne j}}^n\frac{a-a_i}{a_i-a_j}$$ or should I work out some ...