Tagged Questions

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

180 views

Getting $e$ closer than $0,001$?

Everyone knows that $\sum \frac{1}{n!} =e$. How should I make a program in Wolfram Mathematica, that tells me, how many members I need from the sum, to get a number, with mistake smaller, than ...
76 views

Infinite sum not evaluated unless split into even and odd terms

This sum s = Sum[Gamma[k/2]/(2 k!), {k, 1, ∞}] $\sum _{k=1}^{\infty } \frac{\Gamma \left(\frac{k}{2}\right)}{2 k!}$ is returned unevaluated (version 10.1.0). ...
34 views

Sum of operations involving an arbitrary number of 2D vectors

I need to define an equation stating that the sum of n operations involving n 2D vectors and ...
340 views

Summa package problem

I need to use the features of the Summa package but it doesn't work in Mathematica 9. It gives the error Cannot open UtilitiesFilterOptions My question is: ...
114 views

Need to take infinite sum of residues, is there a way to choose the order of operations for ReleaseHold?

I'm computing an infinite sum of residues. I want to do something like this: ...
238 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
2k 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 ...
76 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
84 views

symbolic summation involving kronecker delta

I have to perform symbolically summations of this kind $\sum_{ijkl} V_{ijkl} c_i c_j c_k \delta_{l,m}$ where $V_{ijkl}$ are quantities which depend on 4 indices and $\delta_{l,m}$ is the kronecker ...
94 views

Wrong output from Mathematica when evaluating a summation

Consider the sum $$\sum_{r=0}^n \binom{n-r-1}{n-r}$$ This sum is not zero because when $r=n$, the result is $\binom{-1}{0} = 1$. However, plugging this formula into Wolfram Alpha does return zero. ...
143 views

Strange NSum behavior

If I do: NSum[(i + 1)/(i + 2) LegendreP[i, 0] LegendreP[i, 0], {i, 0, Infinity}] I get: 1.25216 If I do: ...
239 views

Symbolic sum of Stirling numbers gives wrong answer

Bug introduced in 9.0.1 or earlier and persisting through 10.3.0.0 or later This issue originated from my attempt to answer a question on MathOverflow: ...
58 views

Follow-up to “How to differentiate formally?”: Efficiency concern

In link to "how to differentiate formally?" and particularly to the answer by @Jens, I want to do something like this: ...
101 views

Anyway to speed up my plot of two lines?

My code takes very long time to plot these two lines. But it is very quick when I use Integrate instead of Sum in the formulation. But the there is a constant difference between using Integrate and ...
102 views

Relevant help page for: Sum?

When I type Sum into Mathematica, it also offers Sum in the autocomplete dropdown, but when I click the little menu button next ...
71 views

evaluation of the sum of KroneckerDelta

I need help. I need to know why the next code doesn't simplify in Mathematica 10 but it does in Mathematica 8. I need some similar in version 10. What can I do? ...
87 views

How do I solve for a variable inside a sum but independent of the summation index?

How would I go about solving the following for c? Solve[0 == Sum[(t[i]*m[i] - c*t[i]^2)/s[i]^2, {i, 1, n}], c, Reals] I get ...
118 views

Follow up: how to evaluate this double sum quickly

This question is a follow-up to my previous question. The code I use at the moment is the following: ...
74 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
452 views

Performing Computations on Sets

I would like to find a permutation of $\quad S=\{\frac{1}{10}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{2}{3} \}\quad$ that maximizes the sum of theses elements raised to unique powers: ...
230 views

Is this a bug of NSum?

Check this: NSum[Log[Abs[m]],{m,1,24}] (*54.7847*) NSum[Log[Abs[m]],{m,1,25}] NSum::nsnum: Summand (or its derivative) (Abs^[Prime])[m]/Abs[m] is not ...
308 views

sudden increase in timing when summing over 250 entries

I see a sudden increase of Timing by a factor of thousands when I sum over 250 elements of a matrix rather than over 249. So for instance, this table contains sums ...
120 views

Programming a MaxMin Linear Optimization

I want to program a function for a two-player game. Basically it's like this: . Each player has an array of options, and the result of the game is based on both players choices. So heres my most ...
119 views

Why does this simple sum function fail to compile?

Consider the following compiled function, which takes a $12 \times 5$ array $x_{ij}$ of real numbers and computes the triple sum $$\sum_{k=1}^5 \sum_{i=1}^{12} \sum_{j=i+1}^{12} x_{ik} x_{jk}.$$ ...
268 views

Sum of positive terms gives negative answer

Bug introduced in 7.0 and fixed in 9.0 Mathematica evaluates Sum[((n - y - 1)*(n - y)^2*n^y)/y!, {y, 0, n - 2}] as -2 e^n n. ...
369 views

Bug in splitting sum

I was trying to evaluate the following sum. $$\frac{2}{m}\sum_{\substack{\text{odd }k\\1\leq k\leq m-1}} f(\frac{m+2+\sqrt{m^2-4k+4}}{2})+f(\frac{m+2-\sqrt{m^2-4k+4}}{2}).$$ And I wrote the ...
180 views

Is there an easy way to speed up this double summation in Mathematica

I would like to make an intensity plot of Bosons in a harmonic trapping potential. Hence, I would like to execute the following double summation (everything made dimensionless) for as many terms as ...
48 views

Problem with precision of fraction numbers

I have tried to take a series of harmonic numbers using Mathematica and its precision but there has been an issue. So far when I computed the sums at a whole numbers using a precision of 100 digits I ...
62 views

Problem with calculating Harmonic Numbers

I have tried to take a series of Harmonic Numbers using mathematica but there have been issues in calculations. So far when I computed the sums at a small value range such as ...
75 views

How to make x^0 be 1 as x->0 in a power series?

I'm trying to so this: s[x_] := Sum[a[j]*Sum[a[k]*k*x^(k - 1), {k, 1, Infinity}]^j, {j, 1, Infinity}]; s[0] It returns a 0^0 indeterminacy warning. But a human ...
38 views

Plotting a partial sum (Fourier Series) [closed]

This is what I'd like to plot: ...
143 views

Plotting a Taylor series of Partial sum

Hi people, I want to plot the partial sum from n=0 to n =6 with the given function f about the point a=0 (just the maclaurin series). Unfortunately, I am unable to make sense of the issue M'tica is ...
63 views

WorkingPrecision in a sum

If I am interested in getting a fairly precise plot of f2 below, can I use WorkingPrecision to do this? ...
84 views

Multiple Constrained Sum

I need to perform a multiple summation, that obeys some conditions. This arises in the study of a statistical physics model. q=Exp[-β]. I would like to ask if ...
90 views

43 views

Sum of hypergeometric functions, variable number of arguments

How can I write in Mathematica an expression like this? $$\sum_{k=1}^n {_{k}F_{k}} (1,1,\dots,1; \,2,2,\dots,2; \,z) ~,$$ where ${_{p}F_{q}}$ is the generalized hypergeometric function. My problem ...
252 views

Is it possible to find generating functions of infinite sequences with Mathematica?

I'm trying to find the generating function of a sequence as $(0,1,0,1,0,1,\dots)$ but reading Mathematica's help on FindGeneratingFunction[] seems to tell me that ...
573 views

Sum over multiple indices

I would like to be able to enter the following left hand side of an identity. I can write the right hand side (i think) but am not sure about the left. The Left hand side is ...
107 views

The fastest way of raising indices of high rank tensor

I have some high dimensional high rank tensors, let's say $$F_{ijkl}$$ and I need to find $$F^{abcd}=g^{ai}g^{bj}g^{ck}g^{dl}F_{ijkl}.$$ Here $g^{ij}$ is the contravariant metric. Simple summation ...
Bug introduced in 7.0 and fixed in 9.0.0 According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I ...