Questions using the Sum command, especially for series and other algebraic objects, and related functions such as SumConvergence

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1
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1answer
64 views

How to evaluate sum with different coefficient in each term?

I would like to know if there is a syntax that allows me to enter a sum that has coefficients that vary for every term? I have no interest in evaluating them numerically, but rather to keep them as ...
0
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1answer
34 views

Summing Over a Variable Number of Terms [on hold]

Is there a straightforward way to calculate the following sum ? ...
0
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0answers
46 views

Iteration variable in Sum gets assigned the final iteration value

I've got a function which is defined iteratively via ...
1
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1answer
32 views

series combinations

is there any possibility of displaying all possible series of the form: "1+/-2^2+/-3^2+/-...+/-n^2", where one can choose the sign before the each term and knows the numbers of the terms in the ...
1
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1answer
70 views

Work around bugs in Summation, Hypergeometric function?

I'm so confused I don't even know how to phrase the question, so here's what's happening: I need an analytic form for this: ...
0
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1answer
31 views

Problem with double sum on the calculation of Ricci tensor

I wrote a program in Mathematica to calculate the Riemann and Ricci tensors (obviously, passing trought Christoffel symbols first), however just later I thought of calculating Ricci tensor directily ...
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0answers
43 views

Is there a way for me to get Mathematica show its steps? [duplicate]

I have seen similar questions but they were quite dated (3+ years). When performing, say an Integration, it would be beneficial to see the major steps such as variable substitution, change the order ...
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1answer
56 views

How do you stop Mathematica from evaluating a sum? [closed]

A concentration $A(i,j)$ varies over i,j. I'd like to include the summation of $A(i,j)$ in my Mathematica expressions, but it evaluates the sum ...
2
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1answer
54 views

Error from Compile with a sum over two indices

I have the following code: ...
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1answer
75 views

Multiply out product of sums

For a specific quantum mechanical problem I need to multiply out operators in order to calculate a trace by hand. For example I need a Hamiltonian squared with $H^2$. The Hamiltonian contains of a few ...
9
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2answers
220 views

How to implement symbolic Ramanujan's summation in Mathematica?

How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...
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0answers
77 views

Real part of a sum

I would like to take the real part of the following expression: Sum[(a[i] + I b[i]) r^i/(r^2 + z^2)^i, {i, 0, 2 n}] where all of ...
2
votes
3answers
61 views

Referring to the components of a vector within a sum

I feel like I'm missing something obvious here, but.... I'm playing around, trying to do the standard deviation for my stats homework (don't worry, I already worked out the answer by hand), and I ...
1
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2answers
100 views

Collect distributed sums

I have another task that somehow should be trivial. Suppose I have the following expression $$ \sum_{i=1}^n \frac{2}{9} x_i + 2 \sum_{i=1}^n \frac{1}{9} x_i, $$ or in Mathematica-FullForm ...
4
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1answer
105 views

Converting a sum into $\Sigma$ notation

I have a simple expression of the form $\quad \quad t^5+t^4+t^3+t^2+t+1$ and I want Mathematica to convert this to the form $\quad \quad \sum _{i=0}^5 t^i$ Is there a way to do this?
2
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0answers
35 views

Simplifying symbolic multiple sums

suppose I have a multiple sum with an unspecified number of indexes: $$\sum_{i_1=1}^n \ldots \sum_{i_k=1}^n x_{i_1}\otimes\ldots\otimes \hat{x_{i_j}}\otimes\ldots\otimes x_{i_k}$$ with $x_{i_j}$ ...
3
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1answer
36 views

Apply a list to a summation expression

I've gotten unexpected (at least to my novice eyes) application of a list of values to a Sum expression where the variable for imax is also used in the expression ...
1
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1answer
92 views

Summing terms in Table

I have a table that looks like Table[m, {k, 10}, {j, k}, {i, j}] where, m is a square matrix that depends on the indices $i, ...
0
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1answer
71 views

Strange evaluation of an sum involving binomial coefficients

I stumbled upon this problem while playing with Mathematica 10. Can anyone help me explain the following behaviour? I define a sum ...
6
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1answer
82 views

Sum over Binomials and Gammas

Given the function, ...
2
votes
2answers
164 views

Strange result of an infinite sum

I have the following definition: o[a_] := Sum[ x^(2 k + 1) Product[(2 i + 1)^2 - a^2, {i, 0, k - 1}]/((2 k + 1)!), {k, 0, Infinity}] Now when I evaluate ...
3
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0answers
63 views

Decrease computation time of module [closed]

I need to compute the exponential of a matrix (in this caseR) by the summation method where R is a square matrix with symbolic ...
0
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1answer
49 views

Weird results of calculating a sum of binomials?

In[1]:= Sum[(-1)^k*Binomial[n, k]*Binomial[k, j], {k, 0, n}] Out[1]= (j Binomial[0, j])/(j - n) According to this output, for any ...
1
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2answers
53 views

Infinite Sum with exclusion

From another question I tried to implement something like: Sum[r^(1 - l[n]) DD[n], {n, Complement[Range[1, Infinity], {4}]}] but this does not work because ...
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1answer
46 views

Truncate a sum in a 'smart' way

Consider a series like this: $$\sum_{n=1}^{\infty} (c_n r^{2-n/2}+d_n r^{-n/2})$$ Sum[c[n]r^(2-n/2)+d[n]r^(-n/2),{n,Infinity}] I want, now, to keep only the ...
4
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1answer
353 views

How to sum over primes

Apologies in advance for the simplicity of the question, but I can't fathom how to write the following as a sum in Mathemaitca: \begin{align} &\sum_{p}^{a}\sum_{n}^{b}\text{expression} ...
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0answers
76 views

FullSimplify missing trivial rewrite

I'm trying to understand why Mathematica fails to find the Stirling numbers in the second sum below: ...
1
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2answers
37 views

Imploying a sequence in a series

I would like to have the following sequence, $(a)_n$, in a series where $a_0 = 1$ and $a_n = a(a+1)\cdots (a+ n -1)$. The series I have is $$ 2\sum_{n=0}^{\infty}\frac{(1/2)_n}{n!(2n+1)^3} $$ I know ...
0
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1answer
34 views

Derivative inside a Series [closed]

I have a function defined by a sum, which I would like to differentiate. For example: ...
2
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0answers
39 views

Why does Mathematica provide incosistent convergence conditions?

In[1]:= Clear[a, n] In[2]:= SumConvergence[(n^(n - 2))/((a^n)*(n!)), n] Out[2]= Abs[a] > E In[3]:= SumConvergence[(n^(n - 2))/((E^n)*(n!)), n] Out[3]= True All ...
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1answer
40 views

Summation of functions

I want to define a function that is a sum of other functions. For this, I define functions of the form ...
0
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0answers
91 views

Simplifying terms in a Sum expression

I have a sum in the form of pure function s = Sum[f[k], {k, 0, # - 1}] & of perhaps complicated terms f[k]. The terms ...
3
votes
3answers
263 views

fastest way to perform the following summation

I have a vector $A$ with components $A_{i}$, and two matrices $X$ and $Y$ with components $X_{ij}$, and $Y_{ij}$ respectively. What is the fastest way of performing the following summation ...
6
votes
4answers
178 views

Define Function with Sum over a list

I want to define a function that would symbolically look like $$ t(s,\underline{a})=\pi s + \sum_{n=1}^{n_{max}}a_n\sin(n \pi s) $$ (something like a finite Fourier series). Here $s\in [0,1]$ and ...
5
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0answers
56 views

SumConvergence fails in version 10

SumConvergence[(-1)^(n + 1) ((Cos[n^2] + Sin[n + 2])/7^n), n] Mathematica fails to provide a result (true/false) but wolfram alpha works. What should I do ? It ...
0
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1answer
72 views

Replacement of terms/Pattern matching involving products of derivatives of a function

In delving into Ramanujan summation, I'm trying to get a hold of the relations of the form $$\sum_{n=0}^\infty f(n)=\dfrac{h\frac{d}{dx}}{{\mathrm{e}^{h\frac{d}{dx}}}-1}\int_{0}^\infty ...
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0answers
79 views

Writing rules for Einstein summation

I'm trying to write a list of rules for tensor manipulations and in particular, Einstein summation convention. What I've tried, so far is to write something that would take a generic functions with ...
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0answers
36 views

Failed to use SetPrecision

I am calculating the below formula: $$ \text{ER2}(\alpha,\text{K},\text{q})\text{:=}1+\sum _{m=0}^{K-1} \binom{K+\alpha }{m} \sum _{r=0}^m \frac{(-1)^r \binom{m}{r}}{\left(\frac{1}{q}\right)^{\alpha ...
0
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2answers
57 views

Failed to use N[%] for a infinite series

I am trying to evaluate a infinite series: $$ 2 \sum _{l=1}^{\infty } \Re\left(n^{\frac{2 i \pi l}{\log (q)}} \Gamma \left(\alpha -\frac{2 i l \pi }{\log (q)}\right)\right) $$ With the code: ...
1
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1answer
84 views

How to rewrite and possibly speed up a recursive sum?

I have the following for-loop calculating a multiple nested sum ...
1
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1answer
77 views

Computing a Sequence using Recurrence

I posted a similar question earlier today, but unfortunately I realized after several hours that I over-simplified the problem for this forum. There is a very good answer to the Computing a sequence ...
2
votes
3answers
120 views

Computing a sequence by recurrence

I am trying to create a list where each element of the list is calculated using the sum of all previous elements of the list and also uses the $N$th element of another list. The initial value of the ...
2
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3answers
262 views

Sum the coefficient of a series

I am computing the Series expansion (Lauren series) of an integral and I want to sum up the coefficients of the series. ...
6
votes
2answers
100 views

Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
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1answer
154 views

How effectively Mathematica calculates Sum[Sum[a_k k^m, {m, 0, n}], {k, 1, p}] as a function of n?

Suppose that I have a polynomial of order $n$ $$ f_n(k)=\sum_{m=0}^n a_k k^m, $$ where $k$ is an integer and $a_k$ are arbitrary real numbers. Now I want to use Mathemtica to calculate $$ \sum_{k=1}^p ...
0
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1answer
101 views

Sum Over Multiple Indices part 2 [duplicate]

Recently I asked this question as I was trying to see how to write a particular Identity. I asked about how to write the following sum: ...
1
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2answers
322 views

Sum over multiple indices

I would like to be able to enter the following left hand side of an identity. I can write the right hand side (i think) but am not sure about the left. The Left hand side is ...
1
vote
1answer
114 views

Summand is not numerical at some point

I am trying to do some numerical integration with the following codes: ...
0
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0answers
42 views

Regarding Cycles and Lists of Functions

So, I'm trying to determine the Normal Matrix of a Least Squares Aproximation; I have a basis constituted by 8 functions f1,f2...f8; I have 9 points which constitute Datax = {x1,x2...x9} Now, I ...
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2answers
77 views

Infinite sums with Boole and EvenQ

Suppose I am interested in a sum across a set of even numbers, such as: Sum[x, {x, 2, 20, 2}] 110 or ...