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15
votes
2answers
640 views

Sum or Product with Exclusions

Is there a built-in feature for handling things like: $$\sum_{i=0}_{i\ne j}^n\frac{a-a_i}{a_i-a_j}$$ and $$\prod_{i=0}_{i\ne j}^n\frac{a-a_i}{a_i-a_j}$$ or should I work out some sort of ...
13
votes
1answer
225 views

Baffling increase in runtime

Background of my question I discovered Project Euler today, and decided I would work through the problems in Mathematica. I became obsessed with the first problem, which is essentially "sum all the ...
10
votes
5answers
465 views

Double series over primes

I'm very curious if the following double series over primes has a closed form: $$\sum_{k \in \mathcal{P}}\sum_{n \in \mathcal{P}}\frac{1}{k\;n(k+n)^2}$$ where $\mathcal{P}$ denotes the set of all ...
10
votes
4answers
787 views

how to differentiate formally?

I have been wrapping my head around this for a while now and I have not found a solution so far. I want to work with an arbitrary number of variables in mathematica and use some built in functions. ...
9
votes
6answers
390 views

Performing Computations on Sets

I would like to find a permutation of $\quad S=\{\frac{1}{10}, \frac{1}{2}, \frac{4}{7}, \frac{3}{5}, \frac{2}{3} \}\quad$ that maximizes the sum of theses elements raised to unique powers: ...
8
votes
5answers
1k views

Sum all numbers from 1 to 1000 divided by either 2,3,5 or 7

How do I find the sum all numbers from 1 to 1000 divided by atleast one of 2,3,5 or 7? EDIT: I am sorry for complicating this, but I need it to work for 10^11. So anything that requires too much heap ...
7
votes
6answers
646 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 ...
7
votes
2answers
284 views

Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}]

I have an expression 2^n / Sum[ 2^i Binomial[ n - i - 1, 2n/3 - 1], { i, 0, n/3}] ...
7
votes
1answer
83 views

Bug in GeneratingFunction?

According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I obtain ...
6
votes
3answers
694 views

Ways to compute inner products of tensors

One way to evaluate the following sums is combining Table and Sum: $u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$ $q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$ It will look like ...
6
votes
2answers
1k views

How do you put conditions on indices in a sum?

I'm relatively inexperienced with mathematica, so I apologize if this is a trivial question. I want to take a double sum over a function $f(i,j)$ of two indices, of the form $$ \sum_{i = ...
6
votes
1answer
171 views

Summa package problem

I need to use the features of the Summa package but it doesn't work in Mathematica 9. It gives the error Cannot open Utilities`FilterOptions` My question is: ...
6
votes
0answers
133 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 ...
5
votes
1answer
254 views

Problem with creating a large list of tuples

This is a follow-up question from Sum of Multinomial Coefficients I have thought about the meaning of the formula I mentioned and, with help, I implemented the following code: ...
5
votes
1answer
166 views

Summing tensors in mathematica

How do I perform the following summation in mathematica? \begin{equation} \Sigma_{m=1}^5 e_{ijklm}A^{mn} \end{equation} I have the $e_{ijklm}$ tensor of rank 5 in 5 dimension as a array and $A^{mn}$ ...
4
votes
5answers
863 views

How to sum over a List

list = {11.5575, 11.397, 5.52734, 4.0878, 2.54815, 1.86652, 2.55028, 2.14952, 1.6242, 1.34117} I have a list of numbers. How do I make a function that creates a ...
4
votes
2answers
228 views

What causes this strange convergent sum?

N[Sum[1/(x^2 + 1), {x, 1, Infinity}], 5] N[Sum[1/(x^2 + x + 1), {x, 1, Infinity}], 5] 1.0767 0.79815 + 0.*10^-6 I What causes the strange number?
4
votes
3answers
360 views

Why the difference?

When I do the double sum using the sigma notation I get $$1 + \sum_{n=0}^{\infty}\sum_{k = n}^{\infty} \frac{1}{(k+2)k!}$$ $1 + e - \cosh[1]$ When I do the sums as below, I get the expected ...
4
votes
1answer
197 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 ...
4
votes
3answers
132 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 ...
4
votes
2answers
170 views

Numerical sum does not give consistent results

Consider the function ...
4
votes
2answers
144 views

Speed up plot of $\sum_{j\ge1} 2^{-j}(1-2^{-j})^{n-1}$

I'm a beginner at Mathematica. I would like to plot the following function: $${n\over2} \sum_{j\ge1} 2^{-j}(1-2^{-j})^{n-1}$$ However the following code is just too slow: ...
4
votes
3answers
277 views

Summation with constraints

I am trying to do the summation shown below, $\sum_{i_1=0}^{imax_1} \sum_{i_2=0}^{imax_2} \dots \sum_{i_k=0}^{imax_k} f(i_1,\dots,i_k)$ $k$ is a variable. Therefore $i$ and $imax$ are defined as ...
4
votes
2answers
214 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) = ...
3
votes
2answers
241 views

Incorrect value of infinite sum

Wolfram Alpha and Mathematica give an incorrect result (numerically) for the following infinite sum: ...
3
votes
3answers
457 views

Sum of Multinomial Coefficients

Basically, I want to write a function to compute the following sum $f(m,L):=\sum_{0\leq k_1,\cdots, k_n\leq m} \binom{m}{k_1,k_2,\cdots k_n}$ and $\mathrm{supp}(k)=L \subseteq \left \{ 1,...,n \right ...
3
votes
1answer
197 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 ...
3
votes
2answers
263 views

Can I define a function for vectors of arbitrary dimension?

Is it possible to do analytic calculations with Mathematica? For example, I want to compute: $$\partial \frac{\sum_{j=1}^n G_{j} \prod_{k=1}^{j-1} (1 - G_{k})}{\partial G_l}=-\prod_{k\neq l} ...
3
votes
2answers
214 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. Particularly, I define a sum via ...
3
votes
1answer
229 views

Sum and NSum gives different solutions

I'm working on a Mathematica lab for Calc. 2, and I ran into a problem last night. I was trying to calculate the midpoint approximation of the definite integral of ...
3
votes
2answers
502 views

Sum over all permutations

I have n variables and a function that has all of them as variables. n-3 of them in terms of the entries of two lists. The possible entries in the lists $\alpha$ and $\beta$ range from {2,...n-2}. Now ...
3
votes
1answer
173 views

Sum of positive terms gives negative answer

Mathematica evaluates Sum[((n - y - 1)*(n - y)^2*n^y)/y!, {y, 0, n - 2}] as -2 e^n n. This should not be a negative value. ...
2
votes
2answers
174 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? ...
2
votes
2answers
307 views

Efficiently compute double sum

Is there a "Mathematica Way", like Map or Apply to compute the following double sum? $\sum_{i=1}^{N_1}\sum_{j=1}^{N_2} m_i n_j \, f(\tau_{i} \gamma_{j})$ I have already stored the lists ...
2
votes
2answers
106 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 ...
2
votes
2answers
91 views

Automatically generated summation region

In a multiple Sum I need to put an automatically generated summation region. But when I generate the summation region automatically I get a list whose elements are ...
2
votes
1answer
130 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
2answers
107 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
69 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: ...
2
votes
1answer
125 views

How to evaluate the sum over a hyperplane

I have difficulties in evaluating the following expression: $$\sum_{\small n_1+...+n_{k}=m-k}\; \prod_{i=1}^{k}\frac{1}{(n_i+1)(n_i+2)}$$ I have tried the function ...
2
votes
1answer
364 views

Mathematica 9 behavior with derivative of a sum

In: D[Sum[Sin[x],x],x] D[Sum[f[x],x],x] Out: 1/2 Cos[1/2 (-1 - Pi + 2 x)] Csc[1/2] 0 Function f is undefined, but Mathematica 9 counts it as constant? ...
2
votes
1answer
98 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} ...
2
votes
1answer
168 views

Can we give Mathematica hints for symbolic sums and products?

I have this question at MO and I would like to know if we can give hints to get the symbolic sums and products to come out as $\frac{6}{\pi^{2}}\pm\epsilon$ instead of $0.60792710...$ accurate to ...
2
votes
0answers
90 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 ...
2
votes
0answers
72 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 ...
2
votes
0answers
110 views

Double sum over primes [duplicate]

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

A faster way to do sums?

I found out that,it is INCREDIBLY(like 100 times) faster to use Dot instead of Sum,to perform long sums. But I have not been ...
1
vote
2answers
92 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.
1
vote
1answer
214 views

Summation of If statements

The following made me curious. Suppose you want to sum the if statement If[x[i] < 1., x[i]^2, 0.] over i=1,2, i.e. ...