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Questions tagged [summation]

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

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3
votes
4answers
201 views

Conditional Summations

I am not a math major, but for a networking class, I am taking I am required to do summations for probability. I know the logic but I don't know the mathematical theory to make this work. Using ...
3
votes
1answer
40 views

Plot variations in geometric sum within prescribed range

I have a simple geometric sum: Sum[a^(j + 1), {j, 1, k}] which evaluates to (a^2*(-1 + a^k))/(-1 + a) ...
1
vote
1answer
44 views

Find closed form for roots of trig formula

I have the expression Sum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0 I want to find the roots in terms of ...
5
votes
2answers
161 views

Cumulative total of columns in a matrix or table

I have the following: matrix1 = {{a, b, c, d}, {e, f, g, h}, {i, j, k, l}, {m, n, o, p}} (Note that it's the data that matters, not the fact it's defined as a ...
1
vote
1answer
51 views

Summing results of a table

I have a simple table: example1 = Table[N[x^(x/r), 5], {r, 1, 10}, {x, 1, 10}] I want to create a new table ...
2
votes
2answers
64 views

How can I get the simplest result of this sum?

I am trying to find the sum $$\sum _{k=1}^n \frac{k+1}{(k-1)!+k!+(k+1)! }.$$ I tried Simplify[Sum[(k + 1)/(( k - 1)! + k! + (k + 1)!), {k, 1, n}]] and got ...
1
vote
0answers
185 views

Sum over multiindex

I would like to calculate a sum over some multi-indices, that follow a specific pattern. $$\sum\limits_{1\le i_1<i_2<...<i_k\le N} A(k,i_1, i_2, ..., i_k).$$ $A$ is a fix expression of the ...
0
votes
5answers
110 views

Total of summed objects of unequal lengths

I obtained {1}+{0,2}+{0,0,1}from a calculation. Now I need to sum these objects and reach 4. How can I do this? I tried ...
1
vote
1answer
84 views

Is there a way to exclude certain numbers in a sequence?

For example, the sequence of triangular numbers can be expressed as $1/2 [n (n + 1)]$ with $n=1,2,3,4,...$ but is it possible to create a summation of everything remaining $(2,4,5,7,8,9,11,12,13,14,......
7
votes
2answers
307 views

Relabeling of dummy variables

I have the following expression F[p1, p2] a[p1] ** b[p2] - F[p1, p2] a[p2] ** b[p1] where ** is the non-commutative ...
0
votes
0answers
71 views

Summation together

I have the terms: ...
1
vote
0answers
50 views

Symbolic summation with variable bounds and variable number of indices

I wish to compute compute terms like Sum[f[t[j[1]],t[j[2]],...],{j[1],m},{j[2],n},...] for arbitrary positive integer n and any ...
0
votes
1answer
71 views

How to evaluate sum only when the function is specified explicitly?

How does one instruct Mathematica to perform the following infinite sum only if the function U is specified explicitly? ...
1
vote
1answer
73 views

Recognizing Summation Indices in Mathematica

Consider some complicated expression like the following: $$ Q[a,b]Q[a,c]M[a,c]M[a,b]$$ Where the lower case letters are matrix indices. I am looking for a way to make mathematica recognize all the ...
0
votes
1answer
63 views

Minimization of a summation of two functions with respect to two constrained variables

I have a question regarding the minimization of a function, which is a summation of two separate functions, with a discrete list for one of the variables. $S[a,c]= \sqrt{\sum_{b=0,4,8,12,16}{(f[b]-g[...
1
vote
1answer
96 views

Summing over a list

I intend to sum a series over two lists which I generate myself. However, my code is not working. What is the best way to do this? Thanks. Find my code below ...
0
votes
0answers
68 views

Solving a sum involving a distribution

Can anyone help me solve this sum? ...
0
votes
0answers
59 views

how can I solve this sum?

how can I solve this sum? Sum[1/(x[p]-x[q]),{p,1,l},p\[NotEqual]q] I tried these codes but not workin' ...
0
votes
1answer
41 views

Forcing nice positions of summation Σ 's under and overscript in FractionBox

Apologies if this has been asked before. The expression ...
1
vote
1answer
73 views

Summation of terms involving contractions with 3 Levi Civita tensors

I am trying to evaluate this expression: $\epsilon^{abcdef}X^R_a X^S_b X^T_c X^U_d X^V_e X^W_f \epsilon_{RST} \epsilon_{UVW}$ where: $X = \frac{a^2 +b^2-1}{2a} \mathbb 1_6$ and I wrote this code ...
0
votes
1answer
95 views

Compute inner product of using a double sum vector [closed]

I am struggling to create a vector in Mathematica to compute an inner product. The first vector whose elements are generated over the sum over $m$ is $$a = \sum_{m=0}^n\sum_{r=0}^m C_r a_m + \sum_{m=...
0
votes
1answer
114 views

NIntegrate stuck without any warning

My problem is to compute W: ...
3
votes
1answer
188 views

Sum in Mathematica gives extra “+List” [closed]

I am just doing the following sum over a list t = Table[i^2, {i, 10}] Sum[t[[i]], {i, 0, 4}] However, the output is ...
0
votes
1answer
255 views

Need to evaluate a double summation which includes an integral?

Is it possible to evaluate this double summation which includes an integral with Mathematica for some given $r$? $$\sum_{m=-\infty, m\neq 0}^\infty\sum_{n=-\infty, n\neq 0}^\infty m \int_0^{2 \pi} \...
2
votes
0answers
59 views

How to evaluate $\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$ to get $\binom{n+1}{k+1}$?

I evaluate the following summation using mma (Version: 11.2.0.0): $$\sum_{i=1}^{n-k+1} i \binom{n-i}{k-1}$$ ...
1
vote
1answer
64 views

Sum of part of a list that increases in length

I have a list of numbers whose length increases by 1 for every iteration of a loop. I need to take the sum of the last 5 elements of the list, and if the list's length is smaller than 1 I need to have ...
2
votes
1answer
65 views

Nested ordered summation

How can I implement the following sum? Given $n$ and $j<n$: $$\sum_{k_j=1}^{n-1}\sum_{k_{j-1}=1}^{k_j-1}\sum_{k_{j-2}=1}^{k_{j-1}-1}\dots\sum_{k_1=1}^{k_2-1} \phi_{(n-k_j)}[\phi_{(k_j-k_{j-1})}[\...
0
votes
2answers
106 views

Problems with If condition when Pochhammer symbols are zero

There is a formula for the hypergeometric ($_2F_1$) that expresses it as a sum of Pochhammer symbols, times something that reads $$_2F_1(a,b,c;x) = \sum_{i=0}^{\infty} \frac{(a)_i (b)_i}{(c)_i} \frac{...
0
votes
1answer
136 views

Return analytic expression

I would like to evaluate this summation: \begin{align} \sum_{j=1}^{NM}\left[(u_{j_x} + u_{j_y})^2 - 2(1-\rho) u_{j_x} u_{j_y}\right], \end{align} where $NM$ is some number greater than or equal to $...
2
votes
1answer
55 views

Sum using variables then evaluated with values gives different result than sum with values

I'm trying to do a sum symbolically. However, Mathematica is giving me a different result if I do the sum with numbers or symbols. What's causing this error? ...
0
votes
0answers
50 views

Non trivial summation

I want to do the following summation over m going from $-\infty$ to $\infty$. Here $x$ is the position, $t$ is the time, $v_F$ and $v_h$ are velocities, $\beta$ is $...
10
votes
3answers
1k views

How can I compute a Kronecker sum in Mathematica?

There is Kronecker product but there is no Kronecker sum? It seems like a very important features to include. So in the absence of a Kronecker sum function, how can I construct my own Kronecker sum $...
5
votes
2answers
364 views

Expanding a sum without evaluating it [duplicate]

I am currently trying to expand a sum without evaluating it, e.g. $$\sum_{i=0}^5 i^2 = 1^2+2^2+3^2+4^2+5^2$$ So I am trying to create a function ...
8
votes
2answers
577 views

What is wrong with my use of Summation?

I want to compute $r$ according to the following code: ...
0
votes
1answer
90 views

Sum over permuted and unpermuted indices

I would like to write a code to evaluate the following (up to $N=20$) $\sum_{s_1,...,s_N=\pm 1;s_1 \cdot \cdot \cdot s_N=1}\sum_{\sigma\in S_N}\prod_{i=1}^N x_{\sigma(i)}^{s_i \lambda_i}$ There are ...
0
votes
1answer
72 views

Determining the distribution and other characteristics of a variable defined by a recurrence relation

I want to determine the distribution and some other characteristics of a recursive defined variable and need hereby some help/advice. I have the recurrence relation $\qquad X_t = X_{t-1} + \phi (\...
0
votes
2answers
88 views

Algorithm for Swapping indices and simplifying the summand in a double sum [closed]

Say we have something like $$ \sum_{p}^N\sum_{q}^N \cos(p) \sin(q) - \cos(q)\sin(p) $$ usually, in the case like this, the indices p and q can be swapped, and the sum simplifies to 0. I have an ...
9
votes
2answers
119 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
2
votes
1answer
452 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] = \frac{(N\bar{x}...
2
votes
2answers
182 views

How to make lists the same size?

I want to add 19 lists together and then average over them but they are of unequal length. How do I make then all the same length? i.e. make them all the length of the smallest one. My lists are ...
2
votes
1answer
162 views

How to plot this double sum? [duplicate]

I want to plot solution of some physics problem that I solved (for r between 1 and 2 and for f between 0 and Pi). I tried it myself but since I am beginner in using Wolfram Mathematica I have not ...
1
vote
3answers
535 views

Plotting Solution to Heat Equation

By hand, I've solved the heat equation and looking to 3D plot the solution. My function is $$2\sum_{n=1}^{\infty}\frac{(-1)^n}{n}\sin(nx)e^{-111n^2t}$$ The code I've been trying to use to far is <...
0
votes
2answers
141 views

A simple code for conditional double summation?

I wrote a code as follows ...
1
vote
3answers
129 views

Improving the sum over dummy indexes

I have the following tensor ...
2
votes
3answers
185 views

A restricted summation over a function of integer n-tuple

I want to sum over a function of n-tuple like so: $\sum\limits_{a\leq k_1+k_2+...+k_n\leq b}f(\{k_i\}_{i=1}^{n})$ where each $k_i$ is non-negative, i.e. $k_i\geq0 \;\forall\;i $ An Example: Say, ...
3
votes
2answers
149 views

Symbolic representation of a Bézier curve

The Bézier curve is defined by: $$C(t)=\sum_{i=0}^{n} {{n}\choose{i}} t^i (1-t)^{n-i} P_i$$ where the $P_i$ are the control points. I am trying to write it down in Mathematica. What I have is: <...
4
votes
1answer
86 views

sum simplification

I have this sum Sum[-E^(-j (x kx[p] + y ky[q] + z kz[r])) j g w ky[q] Ux[p, q, r], {p, -∞, ∞}, {q, -∞, ∞}, {r, -∞, ∞}] and I would like to pull constants ...
3
votes
2answers
256 views

Sum over partitions of a number

I know only some basics about mathematica. However I need to write down the following sum: $\sum_{\{m_k\}_N}\prod_{k=1}^N\frac{1}{m_k}[T_k(Z(\tau))]^{m_k}$. Where $\{m_k\}_N$ denotes partitions of ...
0
votes
1answer
92 views

Hecke Operator- sum over divisors of a number

I am trying to write out the Hecke Operator; however, I don't know how to sum over all divisors of an integer. Could someone please give me some advice how to do that. Below is the Hecke Operator ...
20
votes
1answer
295 views

Why is “k” in the output of Sum[Log[k]/k^k, {k,1,Infinity}]?

Fixed in 11.3 NSum[Log[k]/k^k, {k,1,Infinity}, WorkingPrecision->50] (* 0.219947267975228664843531307905860703797097130 *) But ...