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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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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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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 ...
44 views

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

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

Solving system of equations with Summation

I have these three equations (eq1, eq2, eq3): ...
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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 ...
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?. ...
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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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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Problems with double Sum

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

Respecting excluded index in sum

I'm using a function involving a sum where some indices are excluded: ...
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 ...
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 ...
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 '...
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). ...
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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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", ...
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 ...
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 ...
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 $1$, ...
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 ...
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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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: ...
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 ...
153 views

Problem with extracting a constant multiplier out of sum

For a generic symbol A[i] 2 Sum[A[i], {i, 1, n}] == Sum[2 A[i], {i, 1, n}] does not return ...
104 views

Checking an interesting result for a sum

If someone is curious I have solved it here: https://math.stackexchange.com/a/3242204/647013 This question is related to this post https://math.stackexchange.com/q/3241994/647013, but I am fairly ...
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What is the principal difference betwen two results of a seemingly similar sums?

Summing Sum[(a^2 + (b + n)^2)^(-1), {n, -Infinity, Infinity}] gives $$\frac{\pi \sinh (2 \pi a)}{a (\cosh (2 \pi a)-\cos (2 \pi b))}$$ whereas summing <...