The tag has no wiki summary.

learn more… | top users | synonyms

15
votes
4answers
2k 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. ...
10
votes
5answers
561 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 ...
6
votes
1answer
236 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: ...
16
votes
2answers
1k 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 ...
6
votes
3answers
1k 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 ...
4
votes
3answers
383 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
1answer
215 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
2answers
679 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} ...
2
votes
2answers
141 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 ...
1
vote
2answers
215 views

Sum over multiple indices

I would like to be able to enter the following left hand side of an identity. I can write the right hand side (i think) but am not sure about the left. The Left hand side is ...
-5
votes
1answer
276 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 ...
7
votes
2answers
301 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
2answers
2k 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 = ...
3
votes
1answer
254 views

How can I speed up this code with multiple sum´╝č

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 ...
3
votes
2answers
269 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
3answers
605 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 ...
2
votes
1answer
130 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] = ...
9
votes
6answers
410 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: ...
5
votes
3answers
243 views

The speed of Sum[] varies strangely

I was curious about the difference in speed between Total and Sum. I found out Total was ...
5
votes
5answers
2k 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 ...
3
votes
1answer
126 views

How do I format Compile[] correctly?

My Mathematica skill is still rusty, so kindly bear with me. I'm having problem formatting expression to compile the function correctly: $\sum _{g=1}^G \sum ...
3
votes
1answer
119 views

Collect terms in a sum

Suppose I have this expression ...
2
votes
3answers
112 views

Computing a sequence by recurrence

I am trying to create a list where each element of the list is calculated using the sum of all previous elements of the list and also uses the $N$th element of another list. The initial value of the ...
2
votes
0answers
112 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
1answer
58 views

Computing a Sequence using Recurrence

I posted a similar question earlier today, but unfortunately I realized after several hours that I over-simplified the problem for this forum. There is a very good answer to the Computing a sequence ...
1
vote
1answer
92 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
1answer
122 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 ...
1
vote
1answer
208 views

function returning 0

Why is my function returning 0? ...