Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
635
questions
0
votes
0answers
14 views
Summation involving complex conjugate pairs [on hold]
Consider the prime counting function
$$\pi(n)=R(n)-\sum_{\rho} R(n^{\rho})$$
where $R$ is Riemann's function (link) and the $\rho$ are the non-trivial zeroes of the zeta function, taken in ...
0
votes
2answers
17 views
Create symmetric array of function values
I have function B[i,j] where i,j are integers.
Then I create array:
b = Array[B, {3,3}]
now I set values of ...
0
votes
0answers
44 views
How to solve this double summation question with an unknown [on hold]
How to solve this double summation with an unknown in the outer sum? Any full step solution to solve this?
1
vote
0answers
42 views
How to evaluate an expression [on hold]
I have a 3-dimensional array of numbers say A. I want to evaluate the following expression.
$\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...
3
votes
1answer
129 views
Mathematica command to convert $\pi^{2n}$ to $\zeta(2n)$
Is there a command on Mathematica that helps me to get the answer of some harmonic series in terms on $\zeta(2n)$ instead of $\pi^{2n}$? Let me give you an example:
The command :
...
1
vote
2answers
73 views
Implement a recursive formula with internal sum
I need to calculate following recursion formula.
I implemented this in MATHEMATICA as follows:
But it always gives errors for $k>0$. Can someone help me to implement this?
...
0
votes
0answers
70 views
1
vote
1answer
77 views
About some hypergeometrical formulas for roots of trinomial and quadrinomial
Please correct my interpretation of formulas by Pietro Majer from post.
For equation $a=x+x^p$
one root is $x=a\sum\limits_{k=0}^{\infty}\frac{(-a)^{(p-1)k}}{(p-1)k+1} {{pk}\choose{k}}$
Wolfram ...
0
votes
1answer
71 views
Integer functions indices in a sum
I have some troubles with plotted A versus p, especially for the function F(s,l,p), I don´t know how deal with the integer functions indices of the sum. How can I input such a sum to Mathematica?. ...
0
votes
1answer
74 views
Simplifying $\left(f\left(x\right)\frac{\partial}{\partial x}\right)^nf\left(x\right)$ into a summation
In case you're wondering how to get differentials to act like operators in Mathematica, I stumbled across a package Carl Woll made to solve this issue in this question. There's a a more recent version ...
1
vote
2answers
77 views
Sum of n sums, Permutations of the indices, how to write them in Mathematica?
I was wondering how to write a function $ F (r, q, n, f) $ in Mathematica, defined in this way:
$$F(r,q,n,f):=\sum_{i_0=1}^q f(i_0) \Biggl(\sum_{i_1=i_0+1}^{q+1} f(i_1)\biggl(\sum_{i_2=i_1+1}^{q+2} ...
1
vote
2answers
71 views
2
votes
1answer
69 views
Product from max to min [closed]
Product[f[i], {i, 1, 4}]
gives us
f[1] f[2] f[3] f[4]
Is there any way I can take the product it will give something ...
0
votes
1answer
40 views
Simplifying sums and showing equality - limitations?
Is it possible to verify the following lhs,rhs involving the sums
are equal, with Mathematica?
I can verify it for individual values of $d$ variable:
...
2
votes
2answers
145 views
How to calculate complicated expression in WolframAlpha
I need to evaluate the limit:
$$\lim_{n\to\infty}\prod_{k=1}^\infty \left(1-\frac{n}{\left(\frac{n+\sqrt{n^2+4}}{2}\right)^k+\frac{n+\sqrt{n^2+4}}{2}}\right).$$
I could not type into WolframAlpha ...
1
vote
2answers
59 views
Summing over indices
Suppose I have a simple equation with indices, like the one shown in the image. How can I use Mathematica to implement it? I am aware of summing when a specific variable changes value of some range, ...
0
votes
0answers
32 views
Simplifying a sum
The expression I'm trying to do something with is
Sum[1/(a!(s-a)!)b^(-(2a+1)/2) Sqrt[\[Pi]](2a)!/(4^a (a)!)Pochhammer[-a,k],{a,k,s}]
where ...
1
vote
1answer
38 views
Mapping function into elements of Sum
I'm trying to set an attribute that's valid for a generic sum, where n and f are arbitrary.
de[A_ + B_] := de[A] + de[B]
de@Sum[f[i], {i, n}]
Is this possible?
...
3
votes
2answers
54 views
Limit of an infinite summation
The above is from Maple 2019.1. Is there a way to achieve the same result from MMA12?
Tried
Limit[Sum[Sqrt[1 + k^2/n^3] - 1, {k, 1, n}], {n -> Infinity}]
...
0
votes
0answers
36 views
Finding $\frac{4}{l}\sum_{m=0 \\ (j+m-1) even}^{j-1}\frac{3j-2m}{\xi_m}\phi_m(x)$
I have tried this
Sum[4 *j* ChebyshevT[m, 2 x/l - 1] /l EvenQ[j + m - 1] , {m, 1,j - 1}, {j, 1, 10}]
But I got 0
1
vote
3answers
69 views
A question about the use of Sum
Suppose I have the following formula. It calculates the average value of $n$ evenly spaces numbers on the range from $L$ to $H$.
...
0
votes
0answers
56 views
Unexpected difference between integral and summation?
I am trying to integrating something like: Integrate[Exp[-i*(k*x+k*z)]*Exp[-(x^2+z^2)],{x,-largenumber,largenumber},{z,-largenumber,largenumber}]
My issue is that ...
1
vote
1answer
75 views
Expectations of sums
I would like to use Mathematica to derive some bounds on empirical estimators, such as $E[Y]$ where $Y = \tfrac1n\sum_{i=1}^n (X_i - X)^2$ and $X = \tfrac1n\sum_{i=1}^n X_i$.
For a moment I thought ...
4
votes
0answers
63 views
Double summation giving unexpected result
The expression (in a notebook with Wolfram Mathematica 12.0.0)
Sum[s[i, j] - s[j, i], {j, b}, {i, b}]
Produces the result
1/2 b EulerPhi[b]
Can anyone ...
0
votes
1answer
41 views
Speed up summation
I want to evaluate the following sum at lots of different values of $R_0$ and $N$ (roughly 100 of each, R0 ranging from 1 to 6, N ranging from 1000 to 10000):
$ \langle Y \rangle = \frac{\sum_{Y=1}^N ...
0
votes
0answers
42 views
Discrete Sum of Function over a Region
I might have completely missed something in my search. I want to discretely sum over a function, $f(x_i,y_j)$ multiplied by some other function $g$ over a general region $S$.
$$\sum_{(x,y)\in S}f(x,...
5
votes
2answers
72 views
How can I help SumConvergence give the right result?
I've been trying to use the SumConvergence on the following series:
SumConvergence[1/(n Log[n] Log[n Log[n]]), n]
This ...
1
vote
2answers
42 views
Problems with double Sum
I have some decent problems with performing a double summation.
The Sum is as follows
...
2
votes
0answers
44 views
Triple infinite summation of a 3D Fourier series
I'm trying to evaluate the equation below excluding the case when $n_x=n_y=n_z=0$. I know this equation converges everywhere except where x,y, and are all multiples of $2\pi$. I've attempted breaking ...
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
64 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
57 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
48 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
44 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
94 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
41 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
66 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
59 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
113 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}$$
I want to create a function that takes this polynomial and does the ...
2
votes
0answers
58 views
Computing Definite Sums of Rational Functions
I am attempting to compute a rather complicated sum, $S_n$, that in the end satisfies the relation $(S_n + T_n) = (\frac{(n+1)^2 - 1}{n+1})m^3 + O(m^2)$. I should note that $T_n$ is also unknown. ...
0
votes
1answer
58 views
Simplify multiple summations involving Kronecker deltas
Sorry if this has been asked before, but I couldn't find a specific answer to it.
These work, i.e. they simplify:
...
1
vote
2answers
70 views
Collecting terms from expression with indexed functions
Say I have an expansion of terms containing functions y[j,t] and its derivatives, indexed by j with the index beginning at 0 ...
3
votes
2answers
153 views
Problem with extracting a constant multiplier out of sum
For a generic symbol A[i]
2 Sum[A[i], {i, 1, n}] == Sum[2 A[i], {i, 1, n}]
does not return ...
1
vote
1answer
104 views
Checking an interesting result for a sum
If someone is curious I have solved it here: https://math.stackexchange.com/a/3242204/647013
This question is related to this post https://math.stackexchange.com/q/3241994/647013, but I am fairly ...
0
votes
0answers
24 views
What is the principal difference betwen two results of a seemingly similar sums?
Summing
Sum[(a^2 + (b + n)^2)^(-1), {n, -Infinity, Infinity}]
gives
$$\frac{\pi \sinh (2 \pi a)}{a (\cosh (2 \pi a)-\cos (2 \pi b))}$$
whereas summing
<...
3
votes
1answer
64 views
What is the meaning of True in my result? [closed]
When I do the sum
Sum[(a + (b + π n)^2)^(-1), {n, -∞, ∞}]
the result reads
$$\begin{array}{cc}
\{ &
\begin{array}{cc}
\frac{\coth \left(\sqrt{a}+i b\...
0
votes
0answers
19 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
199 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
88 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 ...
