Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
2
votes
2answers
53 views
Evaluating a summation while suppressing zero raised to a negative power
I want to compute the following multiple summation.
...
1
vote
2answers
52 views
Why does Sum[Length[Divisors[a]], {a, 1 ,x}] return x?
I am summing the number of divisors and I am getting the strange answer below even where there is no input to this function.
...
0
votes
0answers
75 views
Sum a certain hypergeometric-function-based expression pertaining to an integration problem
I would like to sum over the index $h$ from 3 to $\infty$, the expression
...
1
vote
2answers
84 views
Simplify Kronecker Delta expression
How to obtain Kronecker delta summation rule using Wolfram Mathematica:
$$
\delta_{ij}\delta_{jk}=\delta_{ik}
$$
The following code does not produce the result.
...
0
votes
0answers
57 views
How to sum over the variable in partial derivative operator?
I need to use the partial derivative operator in Wolfram Mathematica within a summation, specifically to define the D'Alembertian operator of scalar fields. I am having trouble summing over the D ...
1
vote
1answer
26 views
Evaluation of Extract and use the result in a Sum
I am experiencing a problem in the evaluation of a sum. I hope that someone can help me, I am not an expert Mathematica programmer. I'm posting just the portion of code that gives problems, I know ...
4
votes
1answer
82 views
Strange result with an indefinite double sum
Bug introduced in V10.0.2 or earlier and persists through V11.3
(Simplified version - courtesy Lukas Lang - reported [CASE:4208776])
I try to compute
...
5
votes
2answers
203 views
If and summation: why do I have the index of the summation in the final result?
Consider the following code:
Sum[If[b != 0, a[m], 0], {m, 1, 4}]
(* 4 If[b != 0, a[m], 0] *)
Why does it return me a[m]? m ...
1
vote
1answer
59 views
Why is the function assuming not taken in consideration?
In the following code, I assume that my variables are strictly positive. However, mathematica doesn't take this in consideration when it evaluates the If : the If is still in a non simplified form.
...
0
votes
2answers
66 views
0
votes
2answers
46 views
Sum over integer partition with variable function argument
Define
$$\hat{X}(Y) = [X,Y]
$$
I have known matrices $S_i$ and $V$. I am trying to use Mathematica to define a function which calculates
$$
\sum_{\substack{n_1, \ldots, n_k>1\\ n_1+\ldots n_k = ...
3
votes
0answers
32 views
Why does this sum return unevaluated when testing for convergence?
Why does Mathematica return unevaluated for SumConvergence[Sin[\[Pi]/n^2], n]? I tried looking at the documentation, but I can't find any possible issues. The ...
2
votes
2answers
125 views
Sums of products with $ n $ variables
I want to be able to compute a function of $ n $ indices which looks as follows
if $ n>2 $:
$$
\sum_{(i=1,j=1,k=1,l=1,...), (i\neq j\neq k \neq l \neq ...)}^{n} x_{i}x_{j}(x_{k}^2+y_{k}^2)(x_{l}^...
1
vote
0answers
54 views
How to study the behavior of this series in Mathematica? [closed]
I need to compute the Von-Neumman entropy of a density matrix in Quantum Mechanics. The density matrix is
$$\rho=\sum_{n=0}^\infty \dfrac{\tanh^{2n-2}r}{2\cosh^2r}\left[\tanh^2r + \dfrac{n}{\cosh^2r}\...
1
vote
1answer
59 views
Harmonic number of $r$ with order $r$ [closed]
Mathematica recently offered me this expression as the result of an evaluation: HarmonicNumber[r, -r]. I initially thought this must be equivalent to ...
1
vote
1answer
73 views
fast sum computation
I would like to compute sum. How is it possible to compute the sum fast?
May be with the help of replacing Sum with NSum or <...
1
vote
1answer
125 views
On double summation with Mathematica
Today I wanted to evaluate this sum using Mathematica:
$$f(a,b):=\sum_{(k,l)\in\mathbb{Z}^2,\ l\ne0}\frac{1}{(2 i k a \pi +
l b) (2 i (k - l) a \pi + l b)}$$
...
0
votes
0answers
27 views
Rearrange Summation and change duplicated indices
I try to transform
$$\left(\sum _{j=1}^J A(j)\right) \sum _{j=1}^J \sum _{k=1}^K B(j,k)$$
to
$$\sum _{j=1}^J \sum _{k=1}^K \sum _{j_{2}=1}^J A(j_{2})B(j,k)$$
The rule would add subscript to ...
0
votes
1answer
32 views
Sums of binomial expressions returns different and sometimes indeterminate expressions
A problem that I encountered multiple times when taking sums over expressions involving binomials, factorials, etc. is that Mathematica (version 11.2) returns indeterminate expressions when it should ...
-1
votes
1answer
59 views
How to extract a coefficient from a sum
Let us consider a sum of specified functions multiplied by coefficients, for example
f[x_]:= Sum[Exp[j*x]*p[j],{j,1,n}]
I want to extract the coefficient ...
0
votes
1answer
43 views
Derivative of sum of elements of array [closed]
I try to get derivative of sum of an array with respect to an element of the array.
$$s = \sum_{i = 1}^{3}A_{i, 1}$$
Evaluate $\frac{\partial s}{\partial A_{1,1}}$
Below is the code.
...
0
votes
2answers
56 views
Create and manipulate list with variable length?
Is there a way to create and manipulate a function of a sum of arbitrary length? Specifically, I'd like to create a function like the following:
...
0
votes
0answers
44 views
NSum: Summand (or its derivative) is not numerical at point
I am experiencing a problem in evaluating the maximum of a function that is defined as a sum
...
11
votes
4answers
245 views
Finite sum not evaluating
Mathematica refuses to evaluate this summation.
Sum[2^(k + 1)^3 - 2^(k - 1)^3, {k, 0, n}]
It just returns the form unevaluated.
$\sum _{k=0}^n \left(2^{(k+1)^...
1
vote
2answers
63 views
Sum of all the n-th numerical evaluation of an integral and its cumulative sum of the square of the n-th value
I wish to compute the expansion coefficient of a wavefunction(i.e. in quantum mechanics) which in itself is an integral, given by
$$b_{n00} = \int^{\infty}_{u = 0} \frac{1}{(n)^{3/2}} L^{1}_{n-1}\left(...
0
votes
1answer
59 views
Sum was simplified and I don't know how it was done
I want to compute the sum
$\qquad \sum_{i=1}^{n+r}(i+1)n^{i-1}(n+1)^{n+r-i}$
However, when I input the expression
...
8
votes
2answers
2k views
Wolfram says sum diverges, but Mathematica gives a numerical value for infinite sum [closed]
Take this sum for example:
$$\sum_{n=2}^\infty\frac1{\log(n!)}$$
Wolfram says that this does not converge by the comparison test. However, when I use Mathematica's ...
1
vote
4answers
102 views
Summation exercise — how can I translate the problem statement into the Wolfram Language? [closed]
I'm new to both Mathematica and this forum, so this will be my first post here. I just got into Mathematica today, and I've been doing some exercises. Up to now things have been going well, but I've ...
11
votes
0answers
86 views
What does that output of Sum mean?
I made the computation
ClearAll["Global`*"];
r = Sum[1/2^(k*n/(k + n)), {k, 1, 2*n}, Assumptions -> n ∈ Integers && n > 0]
and got
...
1
vote
2answers
69 views
Evaluating a formula that uses summations and products of vectors
Could someone tell me how to find beta1?
I have the following data:
I don't know how to write beta1, and I don't find ...
0
votes
1answer
35 views
summation syntax for defining conditions and solving
I am trying to generate datasets for which specific conditions related to the grand mean, group means, and differences among these values hold. I had tried in R, but was hoping that using Mathematica ...
5
votes
2answers
121 views
Why is $\sum\limits_{k=1}^{100} 0.01 $ different than $\sum\limits_{k=1}^{100} \frac{1}{100}$?
Why does evalutating $\sum\limits_{k=1}^{100} 0.01$ not result in 1?
What I get is 1.0000000000000007.
I know that the number 0.01 in binary results in an infinite sequence of zeros and ones, which ...
3
votes
3answers
316 views
Speeding up the calculation of a binomial sum
Is it possible to speed up this calculation?
A[j_, p_, n_] := Sum[Binomial[n, k] p^k (1 - p)^(n - k), {k, 0, j}]
Plot[{A[j, 0.5, 12000]}, {j, 0, 12000}]
Thanks!
1
vote
1answer
56 views
Simplifying a Sum of Fractions by Removing Fractions in Denominators
I have a sum of fractions of the form $x1 - \frac{(x2 + x3)}{(x4 + x5)} - \frac{(x6 + \frac{x7}{x13})}{(x8 - x9 - \frac{x10}{(x11 + x12)})}.$
How might I simplify it to remove fractions from the ...
-1
votes
1answer
44 views
Why i get “Infinite expression 1/0.^5 encountered” in summation?
this is my code
the file
https://drive.google.com/open?id=1foOFbyAnn4buPgHq_LvF5eGjZYm4SEM-
...
1
vote
1answer
42 views
Create list of values with arbitrary index and the use it in a function
I have the following generating functions:
$l_{2i-1}=l_{1}-(i-2)(w+s)$ with $i\geq 2$ and
$l_{2i}=l_{2}-(i-1)(w+s)$ with $i\geq 2$, so the first one is for odd index and the second for even index. ...
3
votes
0answers
76 views
Summation of the multipole expansions [closed]
Let $ \vec\Omega, \vec\Omega' $ be two unit vectors in $ \mathbb R^3 $ such that $ \vec\Omega\cdot\vec\Omega' = t $ and let $ r > 0 $. The multipole expansion for the exponential reads:
$$
\...
3
votes
0answers
151 views
On Ж, and the fine-structure constant
I'm trying to reproduce the results from a certain infamous paper that has been moving around the web for the last few days. The details are irrelevant.
This paper claims to have a closed-form ...
2
votes
1answer
86 views
Computing numerically infinite sum of some double series
Let's consider the series:
$$
F(t) = \sum\limits_{n=0}^{\infty}\sum\limits_{k=0}^{\infty}
\frac{(-b)^k(-a)^n\binom{n+k}{k} t^{2n+k(2-\alpha)}}{\Gamma(2n+k(2-\alpha)+2)}
$$
where $a,b$ are ...
-1
votes
2answers
57 views
Please help me get the ratio of x to y [closed]
I need the ratio of x to y in this equation:
sum [n*(x/10)^n/10^(n-2)] == y from n=1 to ∞
Thank you!
3
votes
4answers
173 views
Conditional Summations
I am not a math major, but for a networking class, I am taking I am required to do summations for probability. I know the logic but I don't know the mathematical theory to make this work. Using ...
3
votes
1answer
36 views
Plot variations in geometric sum within prescribed range
I have a simple geometric sum:
Sum[a^(j + 1), {j, 1, k}]
which evaluates to
(a^2*(-1 + a^k))/(-1 + a)
...
1
vote
1answer
41 views
Find closed form for roots of trig formula
I have the expression
Sum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0
I want to find the roots in terms of ...
5
votes
2answers
117 views
Cumulative total of columns in a matrix or table
I have the following:
matrix1 = {{a, b, c, d}, {e, f, g, h}, {i, j, k, l}, {m, n, o, p}}
(Note that it's the data that matters, not the fact it's defined as a ...
1
vote
1answer
41 views
Summing results of a table
I have a simple table:
example1 = Table[N[x^(x/r), 5], {r, 1, 10}, {x, 1, 10}]
I want to create a new table ...
2
votes
2answers
57 views
How can I get the simplest result of this sum?
I am trying to find the sum $$\sum _{k=1}^n
\frac{k+1}{(k-1)!+k!+(k+1)!
}.$$
I tried
Simplify[Sum[(k + 1)/(( k - 1)! + k! + (k + 1)!), {k, 1, n}]]
and got
...
1
vote
0answers
64 views
Sum over multiindex
I would like to calculate a sum over some multi-indices, that follow a specific pattern.
$$\sum\limits_{1\le i_1<i_2<...<i_k\le N} A(k,i_1, i_2, ..., i_k).$$
$A$ is a fix expression of the ...
0
votes
5answers
99 views
Total of summed objects of unequal lengths
I obtained {1}+{0,2}+{0,0,1}from a calculation. Now I need to sum these objects and reach 4. How can I do this? I tried ...
1
vote
1answer
68 views
Is there a way to exclude certain numbers in a sequence?
For example, the sequence of triangular numbers can be expressed as $1/2 [n (n + 1)]$ with $n=1,2,3,4,...$ but is it possible to create a summation of everything remaining $(2,4,5,7,8,9,11,12,13,14,......
0
votes
0answers
68 views
