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

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4
votes
3answers
168 views

sum involving binomial coefficient

To evaluate $ \sum_{\substack{\text{even }k\\ 2\leq k\leq m-2}} \binom{m-2}{k-1}(k-1) $, where $m$ is an even integer. Running the following in Mathematica 10.3.0 (October 9, 2015) ...
3
votes
1answer
74 views

Euler-Maclaurin summation

I want to compute asymptotic approximations to partial sum of harmonic series in Mathematica, using Euler-Maclaurin summation formula. ...
0
votes
1answer
104 views

Plotting a Double Sum

I am attempting to plot a graph of a function that is the absolute value of the double sum of an exponential function, and I keep getting errors. Here is the code: ...
4
votes
3answers
101 views

incorrect exact sum of a series

Sum[(-1)^m*(1/Binomial[2*m + 2, 2] + 1/Binomial[2*m + 3, 2]), {m, 0, Infinity}] gives the right value -2 + π but the same ...
1
vote
1answer
31 views

Engel expansion

How to define Engel expansion in Mathematica? And find the unique non-decreasing sequence of positive integers $ \{ a_1 ,a_2,a_3,... \}$ , such $$\frac{e}{\pi}=\frac{1}{a_1}+\frac{1}{a_1 ...
5
votes
3answers
212 views

Make a vector of sums of matrix rows

I have a matrix in Mathematica: ...
0
votes
0answers
21 views

Adding a list up to a starting value [duplicate]

The code that i need has a starting value of 5. From this starting value on a list of numbers is added consecutively like this list {-0.1,-0,3,-0.1,0.1,-0.1} ...
4
votes
2answers
57 views

Controlling evaluation in a custom summation function

I'm doing some computations that involve summations with many indices over the same range - consider the simplified example Sum[a[i,j],{i,1,2},{j,1,2}]. To prettify ...
4
votes
1answer
90 views

How to increase the evaluation speed of this somewhat complicated table / matrix operation?

I'd like to calculate the following one-dimensional array: OneDimArray = Table[(Norm[Sum[ MatrixA[[i,j]]VectorB[[j]],{j,N}]])^2,{i,N}] However this takes a very ...
2
votes
1answer
58 views

Constrained Sum evaluation [duplicate]

I need to sum up F[x1,x2,...] over x1,x2,... where I have a constraint: x1+x2+...=n (n=positive integer number). For example, I have F[x1,x2] and x1+x2=3, so for the sum I get F[3,0] + F[2,1] + F[1,2] ...
0
votes
0answers
42 views

Summation with one limit as parameters within summation itself

I want to sum one series with summation limits in which the first one given is a function of the terms within the sum, for example: ...
26
votes
1answer
365 views

$\sum _{k=1}^{\infty } \left\lfloor \frac{5}{5^k}\right\rfloor$ giving wrong answer?

Bug introduced in 7.0 or earlier and persisting through 10.3.1 or later When I try to evaluate the following: $$\sum _{k=1}^{\infty } \Bigg\lfloor \frac{5}{5^k}\Bigg\rfloor$$ using ...
0
votes
2answers
61 views

plotting summation to check for convergence

Our assignment was to enter in a series and check to see if it converges by graphing. However, when I attempt to graph it, I get a bunch of errors that I'm not sure what they mean. Best way to show ...
5
votes
0answers
66 views

What is the underlying algorithm to simplify sums of reciprocals of polynomials?

Flipping through Wolfram's blog entry on Leibniz, W noted Huygens' interview test for the young Leibniz, namely to determine: $$ \sum_{n\ge2} \frac{1}{{n \choose 2}} $$ It's one thing to do this by ...
0
votes
0answers
41 views

Extract coefficients from sum

I would like to extract coefficients of indexed variables from a large sum. The following is an example motivated by linear regression to illustrate the problem. Consider the (unnormalised) log ...
1
vote
2answers
72 views

Sum of a set of elements in a array?

For a function I do this (Integrate over circular range): NIntegrate[x*y Boole[Sqrt[x^2 + y^2] < 3], {x, 1, 5}, {y, 1, 5}] ...
5
votes
2answers
156 views

Why this upvalue doesn't escape from Sum?

Probably a hard question, but I decide to cry out loud :). This is actually another problem I encountered when answering this question. Consider the following transform rule stored as an upvalue: ...
2
votes
5answers
65 views

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 ...
1
vote
0answers
38 views
1
vote
5answers
190 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 ...
5
votes
2answers
87 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). ...
2
votes
1answer
44 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 ...
6
votes
2answers
101 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. ...
2
votes
1answer
102 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 ...
9
votes
1answer
80 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
2
votes
0answers
60 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: ...
6
votes
1answer
105 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 ...
8
votes
1answer
81 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? ...
3
votes
2answers
112 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 ...
0
votes
1answer
81 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
0
votes
1answer
123 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: ...
13
votes
3answers
251 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: ...
4
votes
2answers
143 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 ...
3
votes
1answer
125 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 ...
7
votes
1answer
149 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 $$ \sum_{k=1}^5 \sum_{i=1}^{12} \sum_{j=i+1}^{12} x_{ik} x_{jk}. $$ ...
6
votes
2answers
372 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 ...
6
votes
1answer
201 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 ...
0
votes
1answer
55 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 ...
1
vote
0answers
69 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 ...
0
votes
1answer
57 views

Plotting a partial sum (Fourier Series) [closed]

This is what I'd like to plot: ...
3
votes
1answer
76 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 ...
1
vote
1answer
172 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 ...
4
votes
1answer
232 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 ...
3
votes
1answer
67 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? ...
4
votes
0answers
96 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 ...
2
votes
1answer
99 views

Plotting a partial sum

I am given the Legendre expansion of the first kind. $$f(x)=\sum_{n=0}^{\infty}A_{n}P_{n}(x).$$ I have worked the coefficient to be $$A_{n}=\frac{1}{\left \| P_{n}(x) \right \|^{2}} ...
3
votes
1answer
111 views

Calculate sum of probabilities in multinomial model

The question at hand: On average in every 7th chocoloate egg there is a figure to be drawn from a known list of special figures (e.g 15 distinct pieces) the other draws are on average fails. With ...
3
votes
2answers
106 views

How to deduce the Ramanujan's summation of this series?

I have already asked a similar question about Ramanujan's summation in general but received no good answers. Now I am interested in this exact series: $$\sum _{n\ge1}^\Re (24 n + 12 n^2)$$
3
votes
1answer
107 views

Range of summation in simple Plot seems off

I was trying to reproduce a picture in a book by Havil of the sum, $$s = \sum_{r=1}^{\infty}\frac{\mu(r)}{r}\left(Li(x^{\rho_k/r})+Li(x^{\rho_k*/r})\right) $$ using ...
1
vote
1answer
104 views

How to simplify the equation and speed up the codes for four 100*100 matrices

I have to make a sum over 4 variables. Each variable corresponds to a 100*100 matrix. I want to know how to speed up this code. This problem is related to the previous problem 1 and 2. But now I need ...