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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55 views

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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1answer
65 views

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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24 views

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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1answer
122 views

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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1answer
244 views

How to use Mathematica to simplify this kind of trig sum?

$$ S=\sum_{k=0}^{10}\sin\left(\frac{(2+4k)\pi}{23}\right) =\sum_{k=0}^{10}e^\left(i\frac{(2+4k)\pi}{23}\right) =e^{i\frac{2\pi}{23}}\sum_{k=0}^{10}e^{i\frac{4k\pi}{23}} =e^{iu}\sum_{k=0}^{10}\left(e^{...
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0answers
71 views

Sum over an interval

Suppose I want to sum (some function of n) over all integers n except n = 0. Is there a compact way of doing this other than summing from -infty to -1 and then from 1 to infty or even worse summing ...
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39 views

Plotting Interpretation

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230 views

How to find that limit by mathematica? [migrated]

Limit[Sum[2(2k)^(1/(2k))-k^(1/k),{k,n+1,2n}]-n, n -> ∞] to solve by hand, $$\sqrt[y]y=e^{\frac{\ln y}{y}}\sim1+\frac{\ln y}{y}$$ $$2\sqrt[2k]{2k}-\sqrt[k]k\...
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2answers
105 views

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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1answer
60 views

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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1answer
37 views

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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1answer
64 views

Finding ODE series solution coefficients

I am trying to solve an ODE by subbing in a series form and then looking individually at the coefficients of different powers of the variable. I'm looking at a general form of equation: $$\frac{\...
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1answer
64 views

Programatically generating variables and sum

Given a set of variables, say s1through sn, and a way to generate an expression expr ...
6
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1answer
191 views

Strange result for sum $\sum _{k=1}^{\infty } \frac{\sin (k (k-1))}{k}$

In this sum over $k$ Sum[Sin[k (k - 1)]/k, {k, 1, ∞}] the result still containes the summation index $k$. ...
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0answers
54 views

Getting NSum to go to the right depth in recursive definitions

I wanted to produce some plots of the action of the Gauss shift map on cumulative distribution functions. This means I wanted to plot functions $F_n(x)$, for $0 \leq x \leq 1$, defined by $F_1(x) = x$ ...
4
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1answer
60 views

Symbolic double summation vs nested summations

Take the following code: ...
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1answer
38 views

Continuing summation till the magnitude of the terms become smaller than a value

I've tried to plot the below density plot. But since there is a summation inside the plot and the term inside the summation goes to zero differently for different values of $a$ and $t$, I need to tell ...
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0answers
62 views

Evaluating another symbolic sum

Here I asked about a symbolic sum, and received three very insightful replies (from: მამუკა ჯიბლაძე, Carl Woll and Dr. Wolfgang Hintze) which did the trick. (Thank you again!) Currently I am trying ...
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2answers
58 views

Summations on Variables with subscripts

One of my equations uses a set of variables which ultimately for a set of certain values gives a list of 8 numbers: c=13.9506 (31 - k) following cc(sub k) = Round[Table[13.950621339931203...
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2answers
365 views

Evaluating a symbolic sum

I have read how Mathematica does not have an easy time with symbolic sums, but nevertheless would like to know if anyone can suggest an approach to help Mathematica along. For: ...
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2answers
63 views

Obtaining coefficients of a summation by solving equation

I have obtained from some calculations ...
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0answers
66 views

Unexpected result given by Sum [closed]

Consider the following (minimal?) working example: ...
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2answers
61 views

Select subsets from a list based on a criterion?

Assume we have a set of numbers, for instance $A=\{2,3,4,5,6,7,8,9,10\}$ and we are looking for the sums of reciprocals such that they are less than one. I mean I am looking for all $S_B$'s $$ S_B=\...
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1answer
46 views

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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3answers
364 views

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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57 views

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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1answer
72 views

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 ...
4
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2answers
231 views

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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2answers
58 views

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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1answer
65 views

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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2answers
22 views

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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1answer
51 views

D: Understanding the output of 'n' th derivative of a function involving Exp[1]

I am trying to find the $n^{th$ derivate of a function involving Exp[1] as given below. ...
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0answers
46 views

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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1answer
143 views

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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2answers
96 views

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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75 views

Solving system of equations with Summation

I have these three equations (eq1, eq2, eq3): ...
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1answer
83 views

About some hypergeometrical formulas for roots of trinomial and quadrinomial

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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1answer
76 views

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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1answer
76 views

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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2answers
82 views

Sum of n sums, Permutations of the indices, how to write them in Mathematica?

I was wondering how to write a function $ F (r, q, n, f) $ in Mathematica, defined in this way: $$F(r,q,n,f):=\sum_{i_0=1}^q f(i_0) \Biggl(\sum_{i_1=i_0+1}^{q+1} f(i_1)\biggl(\sum_{i_2=i_1+1}^{q+2} ...
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2answers
79 views
2
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1answer
73 views

Product from max to min [closed]

Product[f[i], {i, 1, 4}] gives us f[1] f[2] f[3] f[4] Is there any way I can take the product it will give something ...
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1answer
59 views

Simplifying sums and showing equality - limitations?

Is it possible to verify the following lhs,rhs involving the sums are equal, with Mathematica? I can verify it for individual values of $d$ variable: ...
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2answers
412 views

How to calculate complicated expression in WolframAlpha

I need to evaluate the limit: $$\lim_{n\to\infty}\prod_{k=1}^\infty \left(1-\frac{n}{\left(\frac{n+\sqrt{n^2+4}}{2}\right)^k+\frac{n+\sqrt{n^2+4}}{2}}\right).$$ I could not type into WolframAlpha ...
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2answers
70 views

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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0answers
35 views

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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1answer
39 views

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? ...
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2answers
59 views

Limit of an infinite summation

The above is from Maple 2019.1. Is there a way to achieve the same result from MMA12? Tried Limit[Sum[Sqrt[1 + k^2/n^3] - 1, {k, 1, n}], {n -> Infinity}] ...
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3answers
72 views

A question about the use of Sum

Suppose I have the following formula. It calculates the average value of $n$ evenly spaces numbers on the range from $L$ to $H$. ...

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