tabulating summation series with restrictions Trying to solve this question for a good 5 hours but remained stuck. My intuition tells me I am missing something trivial that I've overlooked or forgotten. I am restricted only to the function 'table', 'accumulate', 'tableform','total','range',.

Attached are my codes:

4 Table[ ((1 - Cos[n π])/(n π)^3 E^(-n π ξ) Sin[n π η]), {n, 1, 25}]

Length[sumterms3]

Total[sumterms3]

ξ = {0., 0.1, 0.2, 0., 0.1, 0.2};

η = {0.4, 0.4, 0.4, 0.5, 0.5, 0.5}


Edit: I can confirm that if I were to sub xi=0 and eta =0.4 into

 Total[sumterms3]


0.239997 would be produced. However, I am looking for a better way to do so.

TableForm[
Flatten[Table[{η, ξ, 4 Total@Table[((1 - Cos[n π])/(n π)^3 E^(-n π ξ) Sin[n π η]),
{n, 1, 25}]},
{η, {.4, .5}}, {ξ, {0, .1, .2}}], 1],
TableAlignments -> Center,
TableHeadings -> {{}, {"η", "ξ", "u(η,ξ)"}}] If you can't use Flatten[ ] it's a little nastier:

ps = {{0.4, 0.}, {0.4, 0.1}, {0.4, 0.2}, {0.5, 0.}, {0.5, 0.1}, {0.5, 0.2}};
TableForm[
Table[{p[], p[],
4 Total@Table[((1 - Cos[n π])/(n π)^3 E^(-n π p[]) Sin[n π p[]]),
{n, 1, 25}]},
{p, ps}],
TableAlignments -> Center,
TableHeadings -> {{}, {"η", "ξ", "u(η,ξ)"}}] u[\[Eta]_, \[Xi]_] :=
Total[4 Table[((1 - Cos[n \[Pi]])/(n \[Pi])^3 E^(-n \[Pi] \[Xi]) Sin[
n \[Pi] \[Eta]]), {n, 1, 25}]];

list = Partition[
Flatten[Table[{i, j,
u[i, j]}, {i, {0.4, 0.5}}, {j, {0, 0.1, 0.2}}]], 3];

TableForm[list,
TableHeadings -> {None, {"\[Eta]", "\[Xi]", "u[\[Eta],\[Xi]]"}}]

pl = {0., 0.1, 0.2, 0., 0.1, 0.2};
ql = {0.4, 0.4, 0.4, 0.5, 0.5, 0.5};

fun = 4 Table[((1 - Cos[n Pi])/(n Pi)^3 E^(-n Pi p) Sin[n Pi q]), {n, 1, 25}];

res = MapThread[Total[fun /. {p -> #1, q -> #2}] &, {pl, ql}]


{0.239997, 0.177074, 0.130061, 0.250007, 0.185091, 0.136277}

 Grid[Prepend[Transpose[{
pl /. a_Real :> PaddedForm[a, {5, 1}],
ql /. a_Real :> PaddedForm[a, {5, 1}],
res /. a_Real :> PaddedForm[a, {8, 6}]}],
{"p", "q", "u(p,q)"}],
Alignment -> Right, Dividers -> All, Spacings -> {1, 2.5}] I did not use Greek characters, but I hope this answers your question:

sum[z_, v_] := 4 Sum[(1 - Cos[n π])/(n π)^3 Exp[-n π z] Sin[n π v], {n, 1, 25}]

Grid[Flatten[Table[{v, z, sum[z, v]}, {v, {0.4, 0.5}}, {z, {0, 0.1, 0.2}}], 1],
Frame -> All]

• Dear God I forgot about the restrictions of the Homework problem !! – Lotus Dec 3 '15 at 15:06

Just something different (but fundamentally Tuples is useful):

f[x_, y_] :=
4 Composition[Dot @@ # &,
Transpose][{(1 - Cos[# Pi])/(# Pi)^3 Exp[-# Pi x],
Sin[# Pi y]} & /@ Range]


Using Tuples:

TableForm[{#1, #2, f[#2, #1]} & @@@
Tuples[{{0.4, 0.5}, {0,0.1, 0.2}}],
TableHeadings -> {None, {"\[Eta]", "\[Xi]", "u(\[Eta],\[Xi])"}}] 