# 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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### Can I force NSum to sum exactly for many terms?

Is there a way to have NSum perform an exact term-by-term summation, when the number of terms is finite? I have a complicated infinite sum in which each term ...
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### Simple nested sum giving ridiculous answer [closed]

I have produced a minimum working example of the issue I'm facing. I would like to evaluate the following symbol sum, with $n\geq0$: $$\sum_{k=0}^n \sum_{m=0}^{2(n-k)} x^m$$ If I evaluate this sum ...
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### Variant on PrimeZetaP

Mathematica has PrimeZetaP for the prime zeta function $\sum_p \frac{1}{p^s}$ where the sum is taken over all primes. How do I use Mathematica to make an ...
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### Wolfram Language 12 says this absolutely convergent series does not converge. Is there any similar example?

I am reading "Lectures on complex function theory" by Takaaki Nomura. In this book, there is the following example: $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converges absolutely. But ...
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### How to simplify Sum's and Product's of arbitrary length?

I would expect Sum[Subscript[x,i], {i, 1, n}] + Sum[-Subscript[x,i], {i, 1, n}] and ...
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### How to add a number, say, 1 to a random real number in Mathematica? [duplicate]

I wish to add, say, 1 to a random real number, say between 1/3 and 1/6. I have used the following code in Mathematica, but it does not answer properly. code: p := RandomReal[1/6,1/3] q:=p+1 p ...
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### Strange behaviour of infinite sum (H[n]- Series[H[n]])

Bug report filed 14.01.2020 A support case was created with the ID [CASE:4371991] EDIT It is easy to show that the workaround "limit of finite sum" proposed in the solution by user64494 leads to ...
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### Transforming a sum of products of binomial coefficients gives only partially determined expression

On 11.0.1.0, Sum[Binomial[n + 3, i] Binomial[n, k - i] 2^i, {i, 0, k}] gives ...
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### How can I obtain a regularized value of this integral using Mathematica?

I want to know the regularized value of this integral. Wolfram Mathematica fails. $$\int_0^\infty \psi'(x+1)dx$$ I have two conjectures, it is either $\gamma$ or $0$. I attempted ...
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### How to calculate an infinite sum to 100 exact digits with NSum?

In the discussion https://math.stackexchange.com/a/3419778/198592 I stumbled of the question how to calculate the sum $$s= \sum _{n=3}^{\infty } \frac{n \cot \left(\frac{\pi }{n}\right)}{4^{n-2}}$$ ...
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### Upgrade to Mathematica 12 - Sum isn't evaluated in reasonable time anymore

I just upgraded from Mathematica 11.3 to Mathematica 12. Unfortunately, code that previously ran in a reasonable amount of time (say 10 sec or half a minute, does now not complete anymore before I ...
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### Typing and derivating unevaluated sums

First I would like to get the output of F[x_, y_, k_] := Sum[x^(m - n)*y^m, {n, 0, k}, {m, n, k - 1}] as an unevaluated (symbolic) sum. Then, derivate F ...
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### Sum of all matrix entries

For large $n\times n$ symmetric matrices $T,$ where $n\approx10000,$ is there an efficient way of computing the total sum $S$ of its entries in Mathematica without having to loop over all its entries? ...
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### Finding Closed form expressions for sums

I am working with the a problem where I need to compute some complicated sums, for which I first define the following inner product. ...
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### Using Power series notation for equations of motion [closed]

How would I simplify these expressions into power series notation in mathematica? For example, in a 3 body system of the earth moon and sun. Where masses are ...
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### Create symmetric array of function values

I have function B[i,j] where i,j are integers. Then I create array: b = Array[B, {3,3}] now I set values of ...
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### D: Understanding the output of 'n' th derivative of a function involving Exp

I am trying to find the $n^{th$ derivate of a function involving Exp as given below. ...
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### How to evaluate an expression [closed]

I have a 3-dimensional array of numbers say A. I want to evaluate the following expression. $\displaystyle\sum_{\sigma,\tau \in S_6}(\Pi_{i=1}^6A(i,\sigma(i),\tau(i)))$. $S_6$ is the symmetric group ...
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### Mathematica command to convert $\pi^{2n}$ to $\zeta(2n)$ [duplicate]

Is there a command on Mathematica that helps me to get the answer of some harmonic series in terms on $\zeta(2n)$ instead of $\pi^{2n}$? Let me give you an example: The command : ...
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### Implement a recursive formula with internal sum

I need to calculate following recursion formula. I implemented this in MATHEMATICA as follows: But it always gives errors for $k>0$. Can someone help me to implement this? ...
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### Solving system of equations with Summation

I have these three equations (eq1, eq2, eq3): ...
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Please correct my interpretation of formulas by Pietro Majer from post. For equation $a=x+x^p$ one root is $x=a\sum\limits_{k=0}^{\infty}\frac{(-a)^{(p-1)k}}{(p-1)k+1} {{pk}\choose{k}}$ Wolfram ...
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### Integer functions indices in a sum

I have some troubles with plotted A versus p, especially for the function F(s,l,p), I don´t know how deal with the integer functions indices of the sum. How can I input such a sum to Mathematica?. ...
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### Simplifying $\left(f\left(x\right)\frac{\partial}{\partial x}\right)^nf\left(x\right)$ into a summation

In case you're wondering how to get differentials to act like operators in Mathematica, I stumbled across a package Carl Woll made to solve this issue in this question. There's a a more recent version ...
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### Summing over indices

Suppose I have a simple equation with indices, like the one shown in the image. How can I use Mathematica to implement it? I am aware of summing when a specific variable changes value of some range, ...
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### Simplifying a sum

The expression I'm trying to do something with is Sum[1/(a!(s-a)!)b^(-(2a+1)/2) Sqrt[\[Pi]](2a)!/(4^a (a)!)Pochhammer[-a,k],{a,k,s}] where ...
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### Mapping function into elements of Sum

I'm trying to set an attribute that's valid for a generic sum, where n and f are arbitrary. de[A_ + B_] := de[A] + de[B] de@Sum[f[i], {i, n}] Is this possible? ...
Suppose I have the following formula. It calculates the average value of $n$ evenly spaces numbers on the range from $L$ to $H$. ...