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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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1answer
34 views

Using Sum notation for equations of motion

How would I simplify these expressions into sum notation in mathematica? For example, in a 3 body system of the earth moon and sun. Where masses are ...
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0answers
15 views

Summation involving complex conjugate pairs [on hold]

Consider the prime counting function $$\pi(n)=R(n)-\sum_{\rho} R(n^{\rho})$$ where $R$ is Riemann's function (link) and the $\rho$ are the non-trivial zeroes of the zeta function, taken in ...
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2answers
18 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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0answers
45 views

How to solve this double summation question with an unknown [closed]

How to solve this double summation with an unknown in the outer sum? Any full step solution to solve this?
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43 views

How to evaluate an expression [on hold]

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
129 views

Mathematica command to convert $\pi^{2n}$ to $\zeta(2n)$

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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1answer
134 views

How to compute many sums or tables efficiently

I have some questions about programming in Mathematica and I would really appreciate it if you could help me. I wish to plot the following function against the variable X, but to do this, first I ...
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2answers
73 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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1answer
40 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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0answers
70 views

Solving system of equations with Summation

I have these three equations (eq1, eq2, eq3): ...
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1answer
77 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
71 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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2answers
77 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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1answer
74 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
71 views
2
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1answer
69 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 ...
2
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2answers
145 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
59 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
32 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
38 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
54 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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0answers
36 views

Finding $\frac{4}{l}\sum_{m=0 \\ (j+m-1) even}^{j-1}\frac{3j-2m}{\xi_m}\phi_m(x)$

I have tried this Sum[4 *j* ChebyshevT[m, 2 x/l - 1] /l EvenQ[j + m - 1] , {m, 1,j - 1}, {j, 1, 10}] But I got 0
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3answers
69 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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0answers
56 views

Unexpected difference between integral and summation?

I am trying to integrating something like: Integrate[Exp[-i*(k*x+k*z)]*Exp[-(x^2+z^2)],{x,-largenumber,largenumber},{z,-largenumber,largenumber}] My issue is that ...
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1answer
75 views

Expectations of sums

I would like to use Mathematica to derive some bounds on empirical estimators, such as $E[Y]$ where $Y = \tfrac1n\sum_{i=1}^n (X_i - X)^2$ and $X = \tfrac1n\sum_{i=1}^n X_i$. For a moment I thought ...
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0answers
63 views

Double summation giving unexpected result

The expression (in a notebook with Wolfram Mathematica 12.0.0) Sum[s[i, j] - s[j, i], {j, b}, {i, b}] Produces the result 1/2 b EulerPhi[b] Can anyone ...
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1answer
41 views

Speed up summation

I want to evaluate the following sum at lots of different values of $R_0$ and $N$ (roughly 100 of each, R0 ranging from 1 to 6, N ranging from 1000 to 10000): $ \langle Y \rangle = \frac{\sum_{Y=1}^N ...
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0answers
42 views

Discrete Sum of Function over a Region

I might have completely missed something in my search. I want to discretely sum over a function, $f(x_i,y_j)$ multiplied by some other function $g$ over a general region $S$. $$\sum_{(x,y)\in S}f(x,...
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1answer
210 views

What is the underlying algorithm to simplify sums of reciprocals of polynomials?

Flipping through Wolfram's blog entry on Leibniz, W noted Huygens' interview test for the young Leibniz, namely to determine: $$\sum_{n\ge2} \frac{1}{{n \choose 2}}$$ It's one thing to do this by ...
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1answer
136 views

Summing over Prime Factors (without repetition)

Wolfram Mathworld (http://mathworld.wolfram.com/SumofPrimeFactors.html) describes a function sopfr(n), the sum of prime factors, which I currently need. This code doesn't work when I insert it in ...
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2answers
72 views

How can I help SumConvergence give the right result?

I've been trying to use the SumConvergence on the following series: SumConvergence[1/(n Log[n] Log[n Log[n]]), n] This ...
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2answers
42 views

Problems with double Sum

I have some decent problems with performing a double summation. The Sum is as follows ...
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1answer
64 views

using Apply to get iterated Sum

Suppose I want to sum a function, $f(\{m_a\})$, of several variables, $m_a$, $a=1,..,n$, which run over ranges, $1,...,k[[a]]$, however, I do not know $n$ in advance. I thought I could do this using `...
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0answers
44 views

Triple infinite summation of a 3D Fourier series

I'm trying to evaluate the equation below excluding the case when $n_x=n_y=n_z=0$. I know this equation converges everywhere except where x,y, and are all multiples of $2\pi$. I've attempted breaking ...
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1answer
41 views

Respecting excluded index in sum

I'm using a function involving a sum where some indices are excluded: ...
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0answers
69 views

Matheamtica Junior on HPC

I am learning Matheamtica on HPC and have never used a linux system before. I have turned the style "input" into "code" and save the file as m format. However, the HPC does not work. The code is ...
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1answer
64 views

Multiply a Sum by a factor

A very simple question: How can I tell to Mathematica that: $\begin{equation} x*\sum_{k=0}^{\infty}\,b_kx^k=\sum_{k=0}^{\infty}\,b_kx^{k+1}\end{equation} $ I tried to multiply but Mathematica gives ...
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1answer
57 views

How does one use NSum within NIntegrate properly?

If I use symbolic integration for the following: Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}] 336 as one can see it gives the answer as it seems to '...
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1answer
48 views

Error with NSum : it returns NSum::nsnum: Summand (or its derivative) f[n] is not numerical at point n=17

Consider the following example (I had a lot of trouble to find a minimal working example, I think it is compactified enough now). ...
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2answers
44 views

Sum up different arrays into a new array

I have a question regarding sums in arrays. So I have the following array: ...
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1answer
94 views

Calculation of sum $\begin{aligned}\sum_{k = 1}^{n - 1}\end{aligned}\left(1+\cos\left(\frac{k\,\pi}{n}\right)\right)^n$

Having established that Mathematica cannot calculate the following summation: sum = Sum[(1 + Cos[k Pi/n])^n, {k, 1, n - 1}] I implemented the classic "plan B", ...
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1answer
41 views

Modifying/optimizing a double sum with an If condition

I would like to better understand double summations where one of the sums depends on the upper limit of the previous sum. This appears frequently in representation theory (to the extent of my ...
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2answers
66 views

Apparent contradiction in double summation

I have two expressions which, if my maths is correct, should both be true. But Mathematica doesn't agree. I can take the expression E^(-n^3) out of the single ...
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0answers
58 views

Computing Definite Sums of Rational Functions

I am attempting to compute a rather complicated sum, $S_n$, that in the end satisfies the relation $(S_n + T_n) = (\frac{(n+1)^2 - 1}{n+1})m^3 + O(m^2)$. I should note that $T_n$ is also unknown. ...
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1answer
59 views

Sum of powers of zero [duplicate]

I would like to calculate the following sum Sum[0^(k-a), {k, 0, Nin}] for a positive integer $a$. With considering $0^0=1$, my expected answer of the sum is $1$, ...
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3answers
113 views

Sum with variable terms to sum over

Suppose I have a polynomial like this: $$a=x_{j_1} + x_{j_1}x_{j_2} + x_{j_1}x_{j_2}x_{j_3} + ...+x_{j_1}x_{j_2}x_{j_3}...x_{j_n}$$ I want to create a function that takes this polynomial and does the ...
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1answer
221 views

Einstein summation convention for symbolic vector calculus

I am trying to do some vector calculus in Mathematica in index notation form because it gives a clear result that can be compared to pen and paper calculations. Since there is no built in Einstein ...
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1answer
58 views

Simplify multiple summations involving Kronecker deltas

Sorry if this has been asked before, but I couldn't find a specific answer to it. These work, i.e. they simplify: ...
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2answers
70 views

Collecting terms from expression with indexed functions

Say I have an expansion of terms containing functions y[j,t] and its derivatives, indexed by j with the index beginning at 0 ...