Questions tagged [summation]
Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence
662
questions
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1answer
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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 ...
0
votes
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 ...
0
votes
0answers
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 ...
5
votes
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 ...
4
votes
1answer
244 views
How to use Mathematica to simplify this kind of trig sum?
$$
S=\sum_{k=0}^{10}\sin\left(\frac{(2+4k)\pi}{23}\right)
=\sum_{k=0}^{10}e^\left(i\frac{(2+4k)\pi}{23}\right)
=e^{i\frac{2\pi}{23}}\sum_{k=0}^{10}e^{i\frac{4k\pi}{23}}
=e^{iu}\sum_{k=0}^{10}\left(e^{...
-1
votes
0answers
71 views
Sum over an interval
Suppose I want to sum (some function of n) over all integers n except n = 0. Is there a compact way of doing this other than summing from -infty to -1 and then from 1 to infty or even worse summing ...
0
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0answers
39 views
6
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0answers
230 views
How to find that limit by mathematica? [migrated]
Limit[Sum[2(2k)^(1/(2k))-k^(1/k),{k,n+1,2n}]-n, n -> ∞]
to solve by hand,
$$\sqrt[y]y=e^{\frac{\ln y}{y}}\sim1+\frac{\ln y}{y}$$
$$2\sqrt[2k]{2k}-\sqrt[k]k\...
5
votes
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
...
0
votes
0answers
41 views
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
...
2
votes
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 ...
0
votes
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
...
0
votes
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{\...
0
votes
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$.
...
1
vote
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
votes
1answer
60 views
0
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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 ...
1
vote
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 ...
0
votes
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...
12
votes
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:
...
0
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2answers
63 views
Obtaining coefficients of a summation by solving equation
I have obtained from some calculations
...
2
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0answers
66 views
2
votes
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=\...
1
vote
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
...
5
votes
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
$$s= \sum _{n=3}^{\infty } \frac{n \cot \left(\frac{\pi }{n}\right)}{4^{n-2}}$$
...
0
votes
0answers
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 ...
3
votes
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
votes
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? ...
1
vote
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.
...
1
vote
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
...
0
votes
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 ...
0
votes
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.
...
1
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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 ...
3
votes
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 :
...
1
vote
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?
...
0
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0answers
75 views
1
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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 ...
0
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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?. ...
0
votes
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 ...
1
vote
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:
$$F(r,q,n,f):=\sum_{i_0=1}^q f(i_0) \Biggl(\sum_{i_1=i_0+1}^{q+1} f(i_1)\biggl(\sum_{i_2=i_1+1}^{q+2} ...
1
vote
2answers
79 views
2
votes
1answer
73 views
Product from max to min [closed]
Product[f[i], {i, 1, 4}]
gives us
f[1] f[2] f[3] f[4]
Is there any way I can take the product it will give something ...
0
votes
1answer
59 views
Simplifying sums and showing equality - limitations?
Is it possible to verify the following lhs,rhs involving the sums
are equal, with Mathematica?
I can verify it for individual values of $d$ variable:
...
2
votes
2answers
412 views
How to calculate complicated expression in WolframAlpha
I need to evaluate the limit:
$$\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 ...
1
vote
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, ...
0
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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 ...
1
vote
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?
...
3
votes
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}]
...
1
vote
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 $H$.
...
