**499 summation questions.**

ThisSum[1, {k, 1, Infinity}, Regularization -> Dirichlet]gives -1/2, which is right.
This
...

I have the following expressionF[p1, p2] a[p1] ** b[p2] - F[p1, p2] a[p2] ** b[p1]where ** is the non-commutative ...

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'
...

Apologies if this has been asked before.
The expression
...

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 ...

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=...

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

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} \...

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

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 ...

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})}[\...

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{...

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 $...

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?
...

I want to create the sum of two lists/vectors such that every element of the first list is added to every element of the other list. I do not want to get "higher order" sums. To illustrate:
...

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 $...

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 $...

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
...

I'm trying to find how many numbers between 1 and 1000, which are not either prime or the sum of successive primes.
I've managed to create the list of all the primes between 1 and 1000:
...

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 ...

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 (\...

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 ...

Bug introduced in 8.0 or earlier and fixed in 9.0
I have:
...

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}...

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 ...

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 ...

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<...

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, ...

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:<...

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 ...

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 ...

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 ...

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

Suppose that I have a polynomial of order $n$
$$
f_n(k)=\sum_{m=0}^n a_k k^m,
$$
where $k$ is an integer and $a_k$ are arbitrary real numbers. Now I want to use Mathemtica to calculate
$$
\sum_{k=1}^p ...

I would like to compute the dimensions of some small free nilpotent Lie algebras. However, I am totally new to this and I could not figure out how to write the double sum which gives the dimension of ...

I'm computing a recursion of polynomials W[g,n] (which is polynomial in L[1],...,L[n], but keep running into the recursion depth error.
I have determined which part of the recursion is causing this, ...

Let $N(n)$ be a set of integers, which can be presented using first $n$ Egyptian fractions:
$$
N(n):=\{m\in\mathbb{Z}:\ \ m=\sum_{i=1}^n\frac{\epsilon_i}{i},\ \epsilon_i=0\ \text{or}\ 1\}
$$
I want ...

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

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 ...

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 ...

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:
...

Suppose I define y = Sum[Subscript[a, k] x^k, {k, 0, Infinity}] which is a power series representation for y. Now if I multiply <...

When I ask Mathematica to evaluateNSum[((-1)^n)/n, {n, 1, 100}]it returns -0.688172 + 2.11297*10^-16 i
Why is this? (-1)^n is either 1 or -1. I don't know why ...

I'm having trouble getting Mathematica (11.0.1.0, OSX High Sierra) to evaluate the following sum:
$\sum_{i=0}^{\infty} f(i) \, g(i) \, \delta_{i,j}$
My code is
...

- simplifying-expressions
- special-functions
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- assumptions
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