- #1
puzzled fish
- 51
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I found this series, when I tried to evaluate the net Newtonian gravitational force on a mass at rest upon one vertex of a cube while all the other masses were arranged on an orthogonal lattice inside the cube:
## \sum\limits_{k=1}^{\infty} \sum\limits_{j=0}^{\infty} \sum\limits_{i=0}^{\infty} \frac 1 {i^2 + j^2 + k^2} ##
I tried to evaluate, ## \sum\limits_{j=1}^{\infty} \sum\limits_{i=0}^{\infty} \frac 1 {i^2 + j^2} ## with a quick VB macro ( Mathematica was very slow ) up to i = j = 500000 and it seems to converge. The amount of calculations for the triple series is enormous, I haven't done it, but it still converges I think.
Sorry, I don't know how to fix this Latex code.
## \sum\limits_{k=1}^{\infty} \sum\limits_{j=0}^{\infty} \sum\limits_{i=0}^{\infty} \frac 1 {i^2 + j^2 + k^2} ##
I tried to evaluate, ## \sum\limits_{j=1}^{\infty} \sum\limits_{i=0}^{\infty} \frac 1 {i^2 + j^2} ## with a quick VB macro ( Mathematica was very slow ) up to i = j = 500000 and it seems to converge. The amount of calculations for the triple series is enormous, I haven't done it, but it still converges I think.
Sorry, I don't know how to fix this Latex code.
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