Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
605
questions
1
vote
1answer
41 views
Respecting excluded index in sum
I'm using a function involving a sum where some indices are excluded:
...
0
votes
0answers
69 views
Matheamtica Junior on HPC
I am learning Matheamtica on HPC and have never used a linux system before. I have turned the style "input" into "code" and save the file as m format. However, the HPC does not work.
The code is ...
3
votes
1answer
61 views
Multiply a Sum by a factor
A very simple question: How can I tell to Mathematica that:
$\begin{equation} x*\sum_{k=0}^{\infty}\,b_kx^k=\sum_{k=0}^{\infty}\,b_kx^{k+1}\end{equation}
$
I tried to multiply but Mathematica gives ...
0
votes
1answer
55 views
How does one use NSum within NIntegrate properly?
If I use symbolic integration for the following:
Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}]
336
as one can see it gives the answer as it seems to '...
2
votes
1answer
42 views
Error with NSum : it returns NSum::nsnum: Summand (or its derivative) f[n] is not numerical at point n=17
Consider the following example (I had a lot of trouble to find a minimal working example, I think it is compactified enough now).
...
1
vote
2answers
41 views
Sum up different arrays into a new array
I have a question regarding sums in arrays.
So I have the following array:
...
2
votes
1answer
91 views
Calculation of sum $\begin{aligned}\sum_{k = 1}^{n - 1}\end{aligned}\left(1+\cos\left(\frac{k\,\pi}{n}\right)\right)^n$
Having established that Mathematica cannot calculate the following summation:
sum = Sum[(1 + Cos[k Pi/n])^n, {k, 1, n - 1}]
I implemented the classic "plan B", ...
0
votes
1answer
33 views
Modifying/optimizing a double sum with an If condition
I would like to better understand double summations where one of the sums depends on the upper limit of the previous sum. This appears frequently in representation theory (to the extent of my ...
0
votes
2answers
63 views
Apparent contradiction in double summation
I have two expressions which, if my maths is correct, should both be true. But Mathematica doesn't agree. I can take the expression E^(-n^3) out of the single ...
0
votes
1answer
58 views
Sum of powers of zero [duplicate]
I would like to calculate the following sum
Sum[0^(k-a), {k, 0, Nin}]
for a positive integer $a$.
With considering $0^0=1$, my expected answer of the sum is $1$, ...
2
votes
3answers
88 views
Sum with variable terms to sum over
Suppose I have a polynomial like this:
$$a=x_{j_1} + x_{j_1}x_{j_2} + x_{j_1}x_{j_2}x_{j_3} + ...+x_{j_1}x_{j_2}x_{j_3}...x_{j_n}$$
I want to create a function that takes this polynomial and does the ...
1
vote
0answers
55 views
Computing Definite Sums of Rational Functions
I am attempting to compute a rather complicated sum, $S_n$, that in the end satisfies the relation $(S_n + T_n) = (\frac{(n+1)^2 - 1}{n+1})m^3 + O(m^2)$. I should note that $T_n$ is also unknown. ...
0
votes
1answer
46 views
Simplify multiple summations involving Kronecker deltas
Sorry if this has been asked before, but I couldn't find a specific answer to it.
These work, i.e. they simplify:
...
1
vote
2answers
62 views
Collecting terms from expression with indexed functions
Say I have an expansion of terms containing functions y[j,t] and its derivatives, indexed by j with the index beginning at 0 ...
3
votes
2answers
146 views
Problem with extracting a constant multiplier out of sum
For a generic symbol A[i]
2 Sum[A[i], {i, 1, n}] == Sum[2 A[i], {i, 1, n}]
does not return ...
1
vote
1answer
101 views
Checking an interesting result for a sum
If someone is curious I have solved it here: https://math.stackexchange.com/a/3242204/647013
This question is related to this post https://math.stackexchange.com/q/3241994/647013, but I am fairly ...
0
votes
0answers
24 views
What is the principal difference betwen two results of a seemingly similar sums?
Summing
Sum[(a^2 + (b + n)^2)^(-1), {n, -Infinity, Infinity}]
gives
$$\frac{\pi \sinh (2 \pi a)}{a (\cosh (2 \pi a)-\cos (2 \pi b))}$$
whereas summing
<...
3
votes
1answer
62 views
What is the meaning of True in my result? [closed]
When I do the sum
Sum[(a + (b + π n)^2)^(-1), {n, -∞, ∞}]
the result reads
$$\begin{array}{cc}
\{ &
\begin{array}{cc}
\frac{\coth \left(\sqrt{a}+i b\...
0
votes
0answers
18 views
Incorrect result with very simple in(de)finite sum of conditionals [duplicate]
The results of both
Sum[If[OddQ[2 m - 1], 1, 0] q^m, {m, n}]
and
Sum[If[OddQ[2m-1],1,0]q^m,{m,\[Infinity]}]
are 0 (in ...
4
votes
1answer
180 views
How to approximate the partial sum formula of a summation to all real numbers using Mathematica?
I am sure one has to use indefinite sums and the Euler-Maclaurin formula.
$$\sum_{x=0}^{n} f(x)=\sum_{x}f(n+1)-\sum_{x}f(0)=\int_{0}^{n+1}f(t) \ dt -\frac{1}{2}f(n+1)+\left(\sum_{k=1}^{\infty}\frac{...
1
vote
2answers
87 views
Sum not recognized as a linear operator by Solve
When I try to solve an equation with a constant under the summation sign, Mathematica does not factor the constant out of the summation and fails to solve a simple equation.
How do I make ...
3
votes
1answer
177 views
How to evaluate sum with one million summands?
For a research project I am working on currently, I need to do a very simple and straightforward calculation. Unfortunately, I do not know how to include Mathematica code here, but it is very short ...
4
votes
3answers
799 views
How to speed up large double sums in a table?
I am calculating a 3-by-3 matrix whose elements are given as follows:
$$
M_{mn} = \frac{1}{N}\sum_{i=1}^N \sum_{j=1}^N (r^i_m - r^j_m)(r^i_n - r^j_n) \tag{1}
$$
where $N$ is the total number of ...
0
votes
1answer
184 views
Why is the result of a Cesaro regularized sum dependant on a mathematically redundant parameter?
I am trying to determine the series
$\qquad \sum_{k=0}^\infty {\rm myCsc}(x,\,\epsilon)\,{\sin(k\,m_C + a_C+\frac\pi 4)}$
where
$\qquad myCsc(x,\epsilon))=
\begin{cases}i\,\epsilon & 0 \...
3
votes
2answers
164 views
How to sum elements of a list of lists?
I know, the title may seem complicated. I have this list:
myList = { {1, 0},{2, 3},{4, 1} }
I want to sum all the sublists (element by element) to obtain this ...
1
vote
1answer
59 views
Using the Sum function square the sums of numbers
How do I use the Sum function for adding and squaring consecutive terms? It's an exercise from Wolfram Challenges.
I want to write my own function that uses the Sum function to get the sum of (1+2)^2 ...
1
vote
1answer
88 views
Efficiently define a function as the numerical result of infinite sums
I want to approximate the solution to the following sum, in such a way that I can plot the function for the variable $\phi$, for a fixed value of $\mu$.
\begin{equation}
f(r(\phi), \mu)=4 e^{-\mu ...
2
votes
2answers
119 views
FullSimplify a trigonometric expression doesn't work as expected
I know this kind of question is frequent asked, yet each case has its own particularities. I will show my problem.
I define the following:
...
1
vote
0answers
57 views
Flaky pattern-matching for Mittag-Leffler sums?
This sum correctly gives the Mittag-Leffler function:
Sum[z^k/Gamma[α*k + α], {k, 0, ∞}]
MittagLefflerE[α, α, z]
Simply factoring the argument of ...
0
votes
5answers
84 views
Sum Over Solutions to an Equation
Two Related Questions
Is there any general built-in functionality for computing a sum over solutions to an equation? This is common in number theory. For example, computing sums of the following form....
2
votes
1answer
35 views
Clarification on how Total[] can be used on multi-dimensional array
I have a rank 5 tensor that ultimately I want to modify so that for the first 3 dimensions, each element is summed together. The result will be a rank 2 tensor whose elements are the summed totals ...
2
votes
1answer
65 views
How to speed up summations with many list callings?
I am trying something similar to the following code with NN as large as a few hundred (at least 100). Now it's very slow and most time is spent on calculating the ...
0
votes
0answers
67 views
Clebsch Gordan coefficients
I'm trying to compute various sums which contain some CG coefficients, where the sum runs over the indexes m1,m2,m corresponding to each of the three angular momenta j1,j2,j. The thing is that when I ...
2
votes
1answer
248 views
The sum of digits of Mersenne primes
I have problem to calculate the sum of digits of the mersenne primes $M_{57885161}$ , $M_{74207281}$ , and $M_{77232917}$. I'm not a 'computer guy', but I know that the sum of digits of $M_{82589933}$ ...
0
votes
1answer
39 views
Handling Errors in Slowly Converging Dirichlet Beta Infinite Sum
I have tried to calculate the following slowly converging double sum in Mathematica 11.3
$$\sum _{k=1}^{\infty } \left(\frac{ 1}{(2 k-1) (2 k+1)} \left(\sum _{n=1}^{\infty } \frac{(-1)^{n-1}}{(2 n-1)...
1
vote
1answer
56 views
Plotting a series
I'm trying to find a way to plot the sum of a series from n to nmax.
Here is the code for the series:
...
0
votes
2answers
99 views
Summation over an index and a set
I have an index CC and a set of values CM, and c is an element of CM and ...
1
vote
0answers
60 views
Sum over cyclic permutation of indices
To define the Schouten bracket I need to be able to sum over a cyclic permutation of the indices:
$$ [\Phi,\Xi]_S=\mathfrak S_{i,j,k} \left(\Phi^{is}\partial_s\Xi^{jk}+ \Xi^{is}\partial_s\Phi^{jk}\...
1
vote
1answer
71 views
Plotting double series
I am new and hoping a warm welcome from this platform.
I am trying to plot the graph of double series in one variable
$$ \sum_{k=0}^{\infty} \sum_{j=0}^{\infty} C_{k,j} \exp(- 3^k 1.5^{j} x)$$
...
0
votes
1answer
54 views
Replace constant in summation function using replace or If or /
Hi i how do i replace constant for k in this summation.
For following:
Even 2*n Even replace k by a
Even 2*n+1 Odd replace k by b
Here is the code
...
1
vote
0answers
80 views
Finding general forms of sums in Mathematica
A general form can be obtained for some sums with binomial coefficients.
Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
2
votes
2answers
50 views
Is it possible to make a series read a separately defined set of values?
I would like to plot a function with a sum in it. Here is the function:
$$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} $$
As you can see, the problem is that I have ...
0
votes
1answer
50 views
using Apply to get iterated Sum
Suppose I want to sum a function, $f(\{m_a\})$, of several variables, $m_a$, $a=1,..,n$, which run over ranges, $1,...,k[[a]]$, however, I do not know $n$ in advance. I thought I could do this using `...
0
votes
3answers
171 views
Subscripted variables with changing subscript
When I want to sum over indexed variables, indices being subscripts, the result works as expected, however, upon loading the Notation package, it doesn't. See below
As one might have expected from ...
0
votes
0answers
66 views
Summation involving 2F2 hypergeometric function
Trying to simplify the following sum:
$$
\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
155 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
6
votes
1answer
173 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
79 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))) ?
...
3
votes
5answers
208 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 ...
