# 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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### 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 ...
2answers
165 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 ...
1answer
154 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 ...
3answers
182 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, ...
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: <...
1answer
82 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 ...
3answers
126 views

### Improving the sum over dummy indexes

I have the following tensor ...
3answers
480 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 <...
2answers
103 views

### Problem when defining a function as a finite sum

I am using Mathematica 8.0.1.0. I defined the following function for use in an answer on math.SE: f[j_] := Sum[1/(j-2k+1)/4^k, {k, 0, Floor[j/2]}] I then used ...
3answers
259 views

### Gravitational potential of a cube

I want to write code that calculates the gravitational potential of an arbitrarily shaped celestial body. To understand the calculation, I started with an easy shape: a rectangle (or a cube). I ...
1answer
71 views

### Abs[.] breaks my infinite sum

The following evaluates correctly to pi^2/4: Sum[n^2 (Sin[n π]/(-1 + n^2))^2, {n, 1, ∞}] The following gives a 1/0 error: ...
1answer
71 views

1answer
137 views

### A hypergeometric sum that fails

Input: Sum[Binomial[k+n-1, n]*Binomial[k, n-k]/k, {k, 1, n}] Output: ...
2answers
82 views

### Infinite sum for all valid triangles triples (a, b, c)

Find the infinite sum of f(a, b, c) = ((2 / 5) ^ a) * ((11) ^ (-c)) * ((7 ^ (-a - b)) for ordered triples(a, b, c) such that a, b, c satisfy the triangle inequality. I simplified the input to a ...
2answers
111 views

### Code to calculate the partial theta function

The version of the partial theta function I want to compute is $O(z) = \sum\limits^\infty_{n=0}\exp(-(z+n\pi)^2)$ Does anyone have or know of code to efficiently compute $O(z)$? There are two papers ...
1answer
59 views

### How to perform this indefinite sum?

The following indefinite sum with (CC[n]=1 for even n and CC[n]=i for odd n) ...
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 ...
1answer
239 views

### Sum of kronecker delta

What else is needed to make Mathematica to simplify the following expression to $z[j]$? Code: ...
2answers
136 views

### A simple code for conditional double summation?

I wrote a code as follows ...
0answers
96 views

### Sum involving hypergeometric function $\mbox{}_1 F_2$

Trying to simplify the sum $$\sum\limits_{n=0}^{\infty}\dfrac{z_1^n}{n!} {}_{1}F_{2}(1;a+n,1-a+n;z_2),$$ where $a\in(0,1)$, $z_1,z_2>0$, and ${}_{1}F_{2}$ denotes the appropriate version of the ...
1answer
71 views