Skip to main content
8 votes
Accepted

Why can't Mathematica compute the series $\sum_{n=1}^{\infty} \frac{\mu(n)}{e^{2n}-1}$?

you can try Sum[(MoebiusMu[k]*q^k)/(1 - q^k), {k, 1, Infinity}] /. q -> Exp[-2] (* 1/E^2 *)
Andreas's user avatar
  • 3,437
8 votes
Accepted

How to derive a closed-form expression for the sum of this series?

Maple: s:=sum(x^(9 + 6*k)/(9 + 6*k)!, k=0..infinity) simplify(convert(s,trig)) Mathematica V 14: ...
Nasser's user avatar
  • 146k
7 votes

Bugs with `Sum`?

Many times in Sum[], n = 0 seems to be a special case connected with bugs. Separate out ...
Michael E2's user avatar
  • 237k
6 votes

Recurrence relation with a sum

RecurrenceTable[ {t[n + 1] == 2 t[n] t[n - 1] + If[n > 1, t[n], 0], t[1] == 2, t[0] == 2}, t[n], {n, 6}] (* {2, 2, 8, 40, 680, 55080, 74963880} *)
Michael E2's user avatar
  • 237k
5 votes

Bugs with `Sum`?

I guess MMA first do the substitution $j\to n-k$, and then there is a bug of Sum for $n=0$ ...
Lacia's user avatar
  • 2,423
4 votes
Accepted

Break summation of terms in summations of each term

Use Distribute, optionally with Expand. ...
Domen's user avatar
  • 27.1k
4 votes
Accepted

Recurrence relation with a sum

...
Bob Hanlon's user avatar
  • 160k
3 votes
Accepted

Double sum error message for NSum

Slow: NSum[1/((2 i + 1)^4 + (2 j + 1)^4), {i, -1000, 1000}, {j, -1000, 1000}, NSumTerms -> 10000] // RepeatedTiming (* {4.82287, 2.1729} *) Somewhat fast:...
Goofy's user avatar
  • 3,277
3 votes

Recurrence relation with a sum

You can use Nest and BlockMap, e.g. ...
ubpdqn's user avatar
  • 62k
3 votes
Accepted

How to use Sum properly to avoid problems when the summating limits are undefined?

When you give non-numeric limits, Sum will actually never see your P[x] = 1 definition, because it will evalute the general term ...
Domen's user avatar
  • 27.1k
2 votes
Accepted

Breaking multiple summations of terms in single term summations

Use a set of replacement rules implementing some simplification rules: ...
march's user avatar
  • 23.9k
2 votes

Breaking multiple summations of terms in single term summations

One way ...
Nasser's user avatar
  • 146k
2 votes

How to find the sum for each individual row in a binary matrix until the first zero is reached from left to right.

Just to participate: using: ...
ubpdqn's user avatar
  • 62k
2 votes

How to find the sum for each individual row in a binary matrix until the first zero is reached from left to right.

...
eldo's user avatar
  • 77.5k
2 votes

Mathematica incorrectly claims an infinite sum doesn't converge

Looks like Mathematica dosen't know how compute this series. Workaround: ...
Mariusz Iwaniuk's user avatar
1 vote

How to use Mathematica to simplify this kind of trig sum?

Surprisingly Wolfram Alpha does quite well for free: ...
George Colpitts's user avatar
1 vote

How to find the sum for each individual row in a binary matrix until the first zero is reached from left to right.

Using PositionSmallest: -1 + First@PositionSmallest[Append[0]@#] & /@ binarym Using ...
vindobona's user avatar
  • 4,901

Only top scored, non community-wiki answers of a minimum length are eligible