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

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1
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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
90 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
48 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
105 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
104 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
82 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
2
votes
0answers
61 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
107 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
102 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
168 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
97 views

Solve equation with sum in it

Have trouble to solve this equation. Anybody knows where're the problems? ...
0
votes
1answer
130 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: ...
14
votes
3answers
277 views

Symbolic sum of Stirling numbers gives wrong answer

Bug introduced in 9.0.1 or earlier and fixed in 10.4.1 This issue originated from my attempt to answer a question on MathOverflow: ...
4
votes
2answers
177 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
128 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
166 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
381 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
243 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
58 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
71 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
87 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
216 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
235 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
73 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
103 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
116 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
126 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
113 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
108 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
110 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 ...
1
vote
2answers
101 views

How can I speed up this code with 4 variables sum

I have to make a sum over 4 variables. My code is very very slow. I want to know how to speed up this code. This problem is related to but different from one previous problem. Any help or suggestion ...
4
votes
4answers
267 views

How to stop a summation when a variable is small enough?

I meet with a problem. I hope to get an infinite summation of $f1(x)/f2(x)$ which converges to zero. So my code is Sum[f1[x]/f2[x],{x,Infinity}] or ...
4
votes
2answers
250 views

Determine the coefficient of expansion of the product of two sumations?

I would like to determine the coefficient of a desired term in the product of two summation where the powers of $x$ are not necessarily integers. For example $$ \sum_{i=1}^N x^{1/i}\sum_{j=1}^N ...
0
votes
1answer
50 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 ...
14
votes
2answers
247 views

Fastest way to sum the upper triangle

I feel like this is an recurring question: if there's a symmetric matrix whose diagonal is not all 0, how could I get the sum of the part of it that's above the diagonal as fast as possible? Small ...
1
vote
2answers
97 views

What can I use as an equivalent of python zip in mathematica inside of Sum[]? [closed]

I want to take two lists of the same length: widths and weights, and sum a function (of 3 variables) over a single index using the elements from both lists that have that index. Then I want to plot ...
5
votes
2answers
139 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 ...
2
votes
1answer
90 views

How should I enter indexed terms? For example, constants $n_k$ for $k\in\{1,\,\ldots,\,N\}$

How should I enter $\quad \quad \sum^{N}_{k=0}{f(n_k)}$ into Mathematica? More generally, how should I work with the indices? Take the following as an example. I know how the ...
3
votes
1answer
110 views

Simplify a huge expression with limited memory

I would like to perform some analytical sums such as the following ...
1
vote
0answers
57 views

How can I get the exact value of this infinite series? [duplicate]

I want to compute the exact value of this infinite series $$\sum_{n=1}^\infty\arcsin{\left(\dfrac{2}{\sqrt{n(n+1)}(\sqrt{n}+\sqrt{n-1})}\right)}$$ I tried to implement something like this ...
2
votes
1answer
56 views

Sum of Products [closed]

What is a way to nest a product in a sum: $$\sum_{i=2}^{N}\cos\theta_i\cos\theta_i^\prime\prod_{j=i+1}^{M}\sin\theta_j\theta_j^\prime$$ where $N$ and $M$ are two numbers? Thank you.
1
vote
0answers
62 views

Does Sum calculate all terms before summing them?

After calculating the sum of a large number of large objects, using B = Sum[RandomInteger[{0, 1}, {10^6}], {100}]; I find that ...
1
vote
0answers
86 views

Improve speed of evaluating a sum over four indices

I am trying to implement the Fox-H function with several variables as sum of residues. I have arrived at the following function; ...
2
votes
1answer
79 views

The Summation of a Summation in Mathematica

I am trying to input $\sum_{a_1=1}^{n-1}$$\sum_{a_2=1}^{{a_1}-1}$$\sum_{a_3=1}^{{a_2}-1}$$\sum_{a_4=1}^{{a_3}-1}$$...f({{a_1},{a_2},{a_3},{a_4}...})$ into Mathematica. The number of sums should be a ...
0
votes
0answers
92 views

Replacing function in Sum

I have this expression, which, after execution, gives these $F[s,r]$ in output. $$ S_{1,1}=\sum _{s=1}^{16} \sum _{r=1}^{16} F(s,r) \text{Tr}\left[G_r.G_1.G_s.G_1\right] $$ Here is a piece of ...
1
vote
1answer
76 views

Weird sum regularization? [duplicate]

I noticed some weird behavior in "Dirichlet" regularization of infinite sums. Let us first compute ...
10
votes
2answers
323 views

Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$

I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$ I tried ...
1
vote
1answer
82 views

Problem in minimizing expression

I am trying to implement bootstrapping (https://en.wikipedia.org/wiki/Bootstrapping_(finance)) of CDS curve. To implement it I am trying to minimize a series of expression. The minimum value of ...
0
votes
2answers
100 views

Solving two variable using two expressions each involving summation

I am trying to solve for h1 and h2 using function solve as in below code, Expression in solve has two equation each equates sum ...