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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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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 ...
75 views

### Perform an explicit summation, if possible, over a restricted range of two indices both varying from 0 to infinity

I would like to sum the term ...
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 ...
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 ...
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?
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 ...
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 : ...
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 ...
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? ...
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: ...
70 views

### Solving system of equations with Summation

I have these three equations (eq1, eq2, eq3): ...
77 views

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?. ...
77 views

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 ...
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 ...
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 ...
42 views

### Problems with double Sum

I have some decent problems with performing a double summation. The Sum is as follows ...
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 `...
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: $$$x*\sum_{k=0}^{\infty}\,b_kx^k=\sum_{k=0}^{\infty}\,b_kx^{k+1}$$$ 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: ...
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", ...
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 ...
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. ...
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 ...
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 ...