Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
1
vote
1answer
57 views
Plotting double series
I am new and hoping a warm welcome from this platform.
I am trying to plot the graph of double series in one variable
$$ \sum_{k=0}^{\infty} \sum_{j=0}^{\infty} C_{k,j} \exp(- 3^k 1.5^{j} x)$$
...
0
votes
1answer
46 views
Replace constant in summation function using replace or If or /
Hi i how do i replace constant for k in this summation.
For following:
Even 2*n Even replace k by a
Even 2*n+1 Odd replace k by b
Here is the code
...
1
vote
0answers
71 views
Finding general forms of sums in Mathematica
A general form can be obtained for some sums with binomial coefficients.
Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
2
votes
2answers
44 views
Is it possible to make a series read a separately defined set of values?
I would like to plot a function with a sum in it. Here is the function:
$$v(k) = \sum_{j=1}^k \frac{v_E \cdot m_j \cdot c}{m_j(1-c)+\sum_{i=j+1}^n m_i} $$
As you can see, the problem is that I have ...
0
votes
1answer
38 views
using Apply to get iterated Sum
Suppose I want to sum a function, $f(\{m_a\})$, of several variables, $m_a$, $a=1,..,n$, which run over ranges, $1,...,k[[a]]$, however, I do not know $n$ in advance. I thought I could do this using `...
0
votes
3answers
79 views
Subscripted variables with changing subscript
When I want to sum over indexed variables, indices being subscripts, the result works as expected, however, upon loading the Notation package, it doesn't. See below
As one might have expected from ...
0
votes
0answers
49 views
Summation involving 2F2 hypergeometric function
Trying to simplify the following sum:
$$
\sum_{i=0}^n\frac{z^i}{(n-i)!}\,\frac{1}{(1+a)_i\,(1-a)_i}\sum_{j=0}^i(-1+a)_j\,(-1-a)_j\frac{(-z)^j}{j!},
$$
where $n=1,2,\ldots$, $z>0$, $0<a<1$, ...
2
votes
3answers
146 views
Force a sum to be simplified
I want to force this sum to be simplified to 1
Sum[Cos[(Pi*l*(2*m + 1))/(n + 1)], {l, 0, n}]
Only DiscretePlot3D gives the correct result showing all point to 1
2
votes
1answer
124 views
Einstein summation convention for symbolic vector calculus
I am trying to do some vector calculus in Mathematica in index notation form because it gives a clear result that can be compared to pen and paper calculations. Since there is no built in Einstein ...
-4
votes
2answers
75 views
Wolfram|Alpha not able to graph sum_(n=0)^∞ (-(ExpIntegralE[-n, (-1 + n) Log[x]] Log[x]^(1 + n))"? [closed]
I know for a fact that nothing in my expression is wrong, then why cant Wolfram|Alph graph:
sum_(n=0)^∞ (-(ExpIntegralE[-n, (-1 + n) Log[x]] Log[x]^(1 + n))) ?
...
2
votes
5answers
145 views
Calculating the Dottie number using an infinite series
The Dottie number is the solution to the equation
$\cos(x) = x$
It is approximately equal to $0.739085133215160641655312.$
This number can be expressed analytically in the following form (see this ...
0
votes
0answers
41 views
Not getting a solution to my maximization problem
I want to solve the following problem:
For $0.5<q<1$, $q<r<1$, $0\leq n$, $0\leq n_1<=\lfloor{n/2}\rfloor$, and $n_1,n\in\mathbb{N}$
calculate $\arg max_{n_1} S(q,r,n,n_1) $ as a ...
2
votes
1answer
31 views
Performance Tuning: Construction of Matrix with Summations
I am trying to solve an eigenvalue problem of a large matrix. The issue is that it takes too much time to construct this large matrix. This is the code that I built:
...
0
votes
0answers
47 views
How do I make this summation work faster?
Is there any way to make this summation be faster?
I previously had spherical harmonics integration which was taking forever to run
How can I do a faster integration?
Using math, I tried to use ...
6
votes
2answers
735 views
How to optimize Mathematica code that depends on eigenvalues of big matrices and big sums?
I've been using Mathematica recently to generate some plots of a few functions. I've been able to get it right after a few questions here.
The resulting code, which works, is this:
...
1
vote
3answers
109 views
Handling cases of cross terms for multi-sums
I have expressions consisting of many multi-sums and I would like to extract cross terms out of them. Consider a simple example:
$$
\sum_{m_1=1}^M \sum_{m_2=1}^M \sum_{m_3=1}^M \sum_{m_4=1}^M (x_{m_1}...
2
votes
1answer
99 views
What am I doing wrong when trying to plot this function?
I'm trying to reproduce the computations of this paper and I'm running into some troubles because I'm rather new to Mathematica.
In the paper's page 4, in figure 2 the authors show a plot of a ...
0
votes
1answer
55 views
Perform an explicit summation, if possible, over a restricted range of two indices both varying from 0 to infinity
I would like to sum the term
...
2
votes
2answers
59 views
Evaluating a summation while suppressing zero raised to a negative power
I want to compute the following multiple summation.
...
1
vote
2answers
55 views
Why does Sum[Length[Divisors[a]], {a, 1 ,x}] return x?
I am summing the number of divisors and I am getting the strange answer below even where there is no input to this function.
...
0
votes
2answers
232 views
Sum a certain hypergeometric-function-based expression pertaining to an integration problem
I would like to sum over the index $h$ from 3 to $\infty$, the expression
...
1
vote
3answers
128 views
Simplify Kronecker Delta expression
How to obtain Kronecker delta summation rule using Wolfram Mathematica:
$$
\delta_{ij}\delta_{jk}=\delta_{ik}
$$
The following code does not produce the result.
...
0
votes
0answers
63 views
How to sum over the variable in partial derivative operator?
I need to use the partial derivative operator in Wolfram Mathematica within a summation, specifically to define the D'Alembertian operator of scalar fields. I am having trouble summing over the D ...
1
vote
1answer
28 views
Evaluation of Extract and use the result in a Sum
I am experiencing a problem in the evaluation of a sum. I hope that someone can help me, I am not an expert Mathematica programmer. I'm posting just the portion of code that gives problems, I know ...
4
votes
1answer
91 views
Strange result with an indefinite double sum
Bug introduced in V10.0.2 or earlier and persists through V11.3
(Simplified version - courtesy Lukas Lang - reported [CASE:4208776])
I try to compute
...
5
votes
2answers
205 views
If and summation: why do I have the index of the summation in the final result?
Consider the following code:
Sum[If[b != 0, a[m], 0], {m, 1, 4}]
(* 4 If[b != 0, a[m], 0] *)
Why does it return me a[m]? m ...
1
vote
1answer
64 views
Why is the function assuming not taken in consideration?
In the following code, I assume that my variables are strictly positive. However, mathematica doesn't take this in consideration when it evaluates the If : the If is still in a non simplified form.
...
0
votes
2answers
66 views
0
votes
2answers
49 views
Sum over integer partition with variable function argument
Define
$$\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
33 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
129 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 $:
$$
\sum_{(i=1,j=1,k=1,l=1,...), (i\neq j\neq k \neq l \neq ...)}^{n} x_{i}x_{j}(x_{k}^2+y_{k}^2)(x_{l}^...
1
vote
0answers
55 views
How to study the behavior of this series in Mathematica? [closed]
I need to compute the Von-Neumman entropy of a density matrix in Quantum Mechanics. The density matrix is
$$\rho=\sum_{n=0}^\infty \dfrac{\tanh^{2n-2}r}{2\cosh^2r}\left[\tanh^2r + \dfrac{n}{\cosh^2r}\...
1
vote
1answer
62 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
75 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
136 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
28 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
33 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
66 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
44 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
63 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
47 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
255 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
64 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
103 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
92 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
73 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
38 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
128 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 ...
