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

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2
votes
1answer
322 views

Symbolic evaluation of the sum of KroneckerDelta

I want to evaluate this simple expression $$ \sum_n f(n)\delta_{mn} = f(m) $$ using this: Sum[KroneckerDelta[m, n] f[n], {n, Infinity}] However Mathematica ...
3
votes
1answer
198 views

Collect terms in a sum

Suppose I have this expression ...
0
votes
2answers
98 views

How do I sum up p items in a sequence?

I have the following sequence list = {p1, p2, p3, p4 ....} I am summing up the p items as follows: p1 + p2 + 2*sqrt (p21*p2) = p12 p12 + p3 + 2*sqrt (p12*p3) = p123 p123 + p4 + 2*sqrt (p123*p4) = ...
0
votes
0answers
68 views

Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
2
votes
1answer
217 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
2
votes
2answers
275 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
3
votes
1answer
72 views

Strange NSum behavior for slightly larger number of terms

For some sums, NSum gives me the result nicely for some number of terms, but if I add one more term, it suddenly becomes much slower. I haven't found the minimum example for which this can be ...
6
votes
3answers
457 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often ...
3
votes
1answer
487 views

How can I speed up this code with multiple sum?

There are 4 variables in this multiple sum, therefore it may take a long time. I have run this program for 12 hours, but no result untill now. I want to know how to speed up this code. Any help or ...
2
votes
0answers
191 views

Computing a sum

I'm trying to make Mathematica compute this sum: Sum[(-1)^k (n - k)^2 Binomial[2 n, k], {k, 0, n}] As is, I get an awful formula: ...
1
vote
1answer
109 views

About doing an sum

I want to explain this summation to Mathematica, For $a >0$ define $n_u, n_d \in \mathbb{Z}$ such that if $\{ a \} \leq 0.5$ then $n_u = [a]-1$ and $n_d = - [a]$ and if $\{ a \} > 0.5$ then ...
4
votes
2answers
165 views

Solve a system of M equations without specifying M

This post has been edited heavily in response to the comments: my initial question was very confusing. I am trying to write my game-theoretic model in Wolfram Language. There is only one remaining ...
5
votes
1answer
383 views

Variable number of nested variable-range sums

I would like to express the following nested sum in Mathematica: $$ S(m,j,N) = \sum_{k_1=m+j-1}^{N-1} f(N,k_1) \sum_{k_2=m+j-2}^{k_1-1} f(k_1,k_2) \cdots \sum_{k_m=j}^{k_{m-1}-1} f(k_{m-1},k_m) $$ ...
1
vote
0answers
77 views

Summing a trig series

I am trying to sum the following expression: (Cos[(2 π m)/N]^2 Cos[(2 π n)/ N])/(2 (Cos[(2 m π)/N] - Cos[(2 n π)/N])) from ...
1
vote
2answers
193 views

Sum does not converge, but I think it should

Why does Mathematica return Sum::div: Sum does not converge. >> When I input Sum[Boole[!IntegerQ[x]], {x, 1, Infinity}] The sum is obviously 0.
7
votes
0answers
185 views

Incorrect evaluation for Thue-Morse signed harmonic series

I would like to evaluate $$s = 1 - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}+\frac{1}{7}-\frac{1}{8} - ... + \frac{(-1)^{\textrm{binary digit sum}(n-1)}}{n} + ... $$ where ...
0
votes
2answers
269 views

What is wrong in my calculation with clebsch-gordan coefficients?

According to theory of angular momentum here must equal one. What's wrong? ...
2
votes
0answers
258 views

Faster Ways to compute recursive summation

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
8
votes
6answers
734 views

Alternating sum

A frog is at the bottom of a 30 metre well. Each day it climbs 5 metres up the side, but it then slips back 3 metres each night. How long does it take to reach the top of the well? Is there an easier ...
1
vote
1answer
149 views

Summation for a function having singularity

I need to do summation of this function with Mathematica. For[t=0,t<500,t++;Sum[-Q*Log[Q],{k,-Infinity,Infinity},{n,-Infinity,Infinity}]] Q= Q1+Q2+Q3 where ...
1
vote
0answers
87 views

Manipulating infinite series

If I type Sum[f[x],{x,m,Infinity}]-Sum[f[x],{x,m+3,Infinity}] I would like Mathematica to return something like ...
1
vote
1answer
156 views

How to assign Subscript[C, i] to a Sum?

What I want to show is: Plot3D[ Sum[1000*Subscript[C, i]^2/(1000*Subscript[C, i] - 600)^r, {i, 1, k}], {k, 1, 30}, {r, 0.1, 1.5}] And, I want the list of ...
1
vote
0answers
38 views

How do I define a tensor from another tensor with summations? [duplicate]

Let's say we have a rank 2 tensor $g_{ij}$. This is basically a list with a Depth of 2. Now I'd like to calculate another tensor ...
2
votes
1answer
163 views

Deriving least-squares equations in Mathematica

I define $Y = a + b*x + e$, and I want to find values for $a,b,$ by least squares, so I minimize $RSS = sum((Y_i - a - b*x_i)^2)$ I then take derivatives, ${d RSS \over da} = 0$ and ${d RSS \over db} ...
1
vote
1answer
191 views

How to define a summation with function calling itself?

I am new to Mathematica. I want to do this f(x)=summation f(t), summation is over t, where 1<=t<=x-1 and mod(x+1,t+1)=1, i.e. when x+1 is divided by t+1, remainder is 1 and f(1)=1. Should i use ...
-5
votes
1answer
566 views

How can I plot a function that is the sum of another function?

I plotted m[t], but actually what I want to plot is g[t], which is a summation of m[t] from ...
0
votes
2answers
122 views

Sum equation with equation and get an equation

I am trying to get an equation from summing other equations but it doesn't result in a correct answer. Is there another way of doing this? ...
2
votes
0answers
83 views

Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity]

I would like to show that the following (and other similar formulae) tends to zero. Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity] What's the right ...
1
vote
4answers
111 views

Question about sum and list in a function

I have a list of this form: $ lst =\left\{\left\{q_1,x_1,y_1,z_1\right\},\left\{q_2,x_2,y_2,z_2\right\},\text{...},\left\{q_n,x_n,y_n,z_n\right\}\right\} $ I want to use this list in the function: ...
2
votes
2answers
177 views

How to exclude numbers in a series and still plot the graph? [duplicate]

I want to plot this: $\displaystyle\sum_{n=-{10}\atop n\ne \pm 1}^{10} \dfrac {4i(-1)^{n}n}{(n^2 - 1)^2}e^{inx}$ but have no idea how I can exclude the cases for when $ n = \pm 1 $. I don't wish to ...
0
votes
3answers
314 views

Mathematica plotting help (plotting a complex fourier series) [duplicate]

How would I plot the following in Mathematica? $ \displaystyle\sum_{n=2}^{10} \bigg(\dfrac {4ine^{inx}(-1)^n}{(n^2 - 1)^2} - \dfrac{4in e^{-inx}(-1)^n}{(n^2 - 1)^2} \bigg) $ Thanks.
2
votes
1answer
131 views

Need to take infinite sum of residues, is there a way to choose the order of operations for ReleaseHold?

I'm computing an infinite sum of residues. I want to do something like this: ...
3
votes
2answers
379 views

Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: ...
2
votes
2answers
259 views

Triple series - evaluation delayed

Trying to figure out if the infinite triple series has a nice closed form. It seems Mathematica is unable to help us here. Numerically, things remain the same, no response. Could you help? ...
1
vote
1answer
138 views

Module that finds the sum of digits of any given positive integer

How can I make a module that finds the sum of digits of any given positive integer? I use this command F[x_]:= Apply[ Plus, IntegerDigits[x] ] Is there another ...
4
votes
1answer
238 views

Summation with jump indices like 1,4,6,9?

I is easy to enter $ \sum_{s=1}^{n}k(s) $ But how can I enter $ \sum_{s=1,3}k(s) $ ? When I try it, Mathematica says ...
2
votes
2answers
134 views

Plot with sum and binomial command

A few days ago I asked about a problem with plotting a sum. You advise me to use Evaluate option, and that helped me very. But now I have a very similar problem, but i can't find the mistake. I have a ...
2
votes
1answer
150 views

Reproducing a Plot done with WolframAlpha [duplicate]

I have problem to draw in Mathematica a plot like this: Plot[{Sum[a^10*(-1)^(x-a), {a, 1, x}]}, {x, 1, 10}] The problem is that on the plot there is no graph. As ...
2
votes
1answer
111 views

Evaluating terms in series

I'm trying to evaluate a simple expression: Subscript[λ, n] = (2 n - 1) π/(2 L); And then sum it up: ...
1
vote
2answers
281 views
1
vote
1answer
95 views

Plotting a sum as a function of its upper bound

Apologies if this is easy to find in the documentation, but is there a quick way of doing the following up to any given 'n'? ...
1
vote
1answer
646 views

Solving a nonlinear system of recurrence equations

I am having two problems regarding Mathematica, and both of them are happening because it does not accept such inputs: ...
4
votes
1answer
512 views

Von Mangoldt function

Can anybody evaluate the following sum for me $$ \sum\limits_{n=2}^\infty(-1)^n\left(\frac{\psi(n)}{n}-\frac{\Lambda(n)}{2n}\right) $$ where $\psi(n)$ is the Chebyshev function and $\Lambda(n)$ is ...
5
votes
2answers
678 views

Problems with Symbolic summation over unknown values

I'm having some real trouble with Mathematica wrongly evaluating various symbolic sums at the moment. I have this function: $$h_{ij}(x) = ...
2
votes
0answers
119 views

Double sum over primes [duplicate]

Can anyone tell me the value of the sum $$\sum_{p\in \mathcal{P}}\sum_{n=1}^{\infty}\frac{\log (p^n)}{2}\left[\,p^{-n}-\psi\left(\frac{p^n+2}{2}\right)+\psi\left(\frac{p^n+1}{2}\right)\right].$$ ...
0
votes
1answer
246 views

Why does Mathematica find a form for this general sum, but not for some special cases?

Today I found a Sum which Mathematica will simplify for a general parameter value $\nu$, but which will not simplify fully for special cases $\nu = 1, 3, ...$ despite the fact that the general answer ...
1
vote
1answer
289 views

Constraint on variables in summation

Is it possible to have a constraint on variables in summation of series just similar to pattern constraint e.g. ...
4
votes
3answers
226 views

Long waiting time for computing a summation

It takes a long time to compute the summation below, and I'd like to know if there are alternative ways to compute things faster. When replacing $15$ by $\infty$, then I should get $3^{1/3}$. I need ...
1
vote
1answer
236 views

function returning 0

Why is my function returning 0? ...