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

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3
votes
1answer
83 views

Range of summation in simple Plot seems off

I was trying to reproduce a picture in a book by Havil of the sum, $$s = \sum_{r=1}^{\infty}\frac{\mu(r)}{r}\left(Li(x^{\rho_k/r})+Li(x^{\rho_k*/r})\right) $$ using ...
1
vote
1answer
84 views

How to simplify the equation and speed up the codes for four 100*100 matrices

I have to make a sum over 4 variables. Each variable corresponds to a 100*100 matrix. I want to know how to speed up this code. This problem is related to the previous problem 1 and 2. But now I need ...
-1
votes
0answers
66 views

problem in solving by Sum

I'm going to solve a problem by using \Sum But as i have many parameter (14) that all are used in sum the running time is awful my program is like this ...
1
vote
2answers
93 views

How can I speed up this code with 4 variables sum

I have to make a sum over 4 variables. My code is very very slow. I want to know how to speed up this code. This problem is related to but different from one previous problem. Any help or suggestion ...
4
votes
4answers
242 views

How to stop a summation when a variable is small enough?

I meet with a problem. I hope to get an infinite summation of $f1(x)/f2(x)$ which converges to zero. So my code is Sum[f1[x]/f2[x],{x,Infinity}] or ...
4
votes
2answers
169 views

Determine the coefficient of expansion of the product of two sumations?

I would like to determine the coefficient of a desired term in the product of two summation where the powers of $x$ are not necessarily integers. For example $$ \sum_{i=1}^N x^{1/i}\sum_{j=1}^N ...
0
votes
1answer
30 views

Sum of hypergeometric functions, variable number of arguments

How can I write in Mathematica an expression like this? $$\sum_{k=1}^n {_{k}F_{k}} (1,1,\dots,1; \,2,2,\dots,2; \,z) ~,$$ where ${_{p}F_{q}}$ is the generalized hypergeometric function. My problem ...
11
votes
2answers
187 views

Fastest way to sum the upper triangle

I feel like this is an recurring question: if there's a symmetric matrix whose diagonal is not all 0, how could I get the sum of the part of it that's above the diagonal as fast as possible? Small ...
1
vote
2answers
51 views

What can I use as an equivalent of python zip in mathematica inside of Sum[]? [closed]

I want to take two lists of the same length: widths and weights, and sum a function (of 3 variables) over a single index using the elements from both lists that have that index. Then I want to plot ...
4
votes
2answers
88 views

The fastest way of raising indices of high rank tensor

I have some high dimensional high rank tensors, let's say $$F_{ijkl}$$ and I need to find $$F^{abcd}=g^{ai}g^{bj}g^{ck}g^{dl}F_{ijkl}.$$ Here $g^{ij}$ is the contravariant metric. Simple summation ...
1
vote
1answer
67 views

How should I enter indexed terms? For example, constants $n_k$ for $k\in\{1,\,\ldots,\,N\}$

How should I enter $\quad \quad \sum^{N}_{k=0}{f(n_k)}$ into Mathematica? More generally, how should I work with the indices? Take the following as an example. I know how the ...
3
votes
1answer
85 views

Simplify a huge expression with limited memory

I would like to perform some analytical sums such as the following ...
1
vote
0answers
54 views

How can I get the exact value of this infinite series? [duplicate]

I want to compute the exact value of this infinite series $$\sum_{n=1}^\infty\arcsin{\left(\dfrac{2}{\sqrt{n(n+1)}(\sqrt{n}+\sqrt{n-1})}\right)}$$ I tried to implement something like this ...
2
votes
1answer
42 views

Sum of Products [closed]

What is a way to nest a product in a sum: $$\sum_{i=2}^{N}\cos\theta_i\cos\theta_i^\prime\prod_{j=i+1}^{M}\sin\theta_j\theta_j^\prime$$ where $N$ and $M$ are two numbers? Thank you.
1
vote
0answers
47 views

Does Sum calculate all terms before summing them?

After calculating the sum of a large number of large objects, using B = Sum[RandomInteger[{0, 1}, {10^6}], {100}]; I find that ...
1
vote
0answers
59 views

Improve speed of evaluating a sum over four indices

I am trying to implement the Fox-H function with several variables as sum of residues. I have arrived at the following function; ...
2
votes
1answer
61 views

The Summation of a Summation in Mathematica

I am trying to input $\sum_{a_1=1}^{n-1}$$\sum_{a_2=1}^{{a_1}-1}$$\sum_{a_3=1}^{{a_2}-1}$$\sum_{a_4=1}^{{a_3}-1}$$...f({{a_1},{a_2},{a_3},{a_4}...})$ into Mathematica. The number of sums should be a ...
0
votes
0answers
67 views

Replacing function in Sum

I have this expression, which, after execution, gives these $F[s,r]$ in output. $$ S_{1,1}=\sum _{s=1}^{16} \sum _{r=1}^{16} F(s,r) \text{Tr}\left[G_r.G_1.G_s.G_1\right] $$ Here is a piece of ...
1
vote
1answer
57 views

Weird sum regularization? [duplicate]

I noticed some weird behavior in "Dirichlet" regularization of infinite sums. Let us first compute ...
10
votes
2answers
249 views

Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$

I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$ I tried ...
1
vote
1answer
66 views

Problem in minimizing expression

I am trying to implement bootstrapping (https://en.wikipedia.org/wiki/Bootstrapping_(finance)) of CDS curve. To implement it I am trying to minimize a series of expression. The minimum value of ...
0
votes
2answers
68 views

Solving two variable using two expressions each involving summation

I am trying to solve for h1 and h2 using function solve as in below code, Expression in solve has two equation each equates sum ...
2
votes
1answer
64 views

Sum over multiple indices that take specific values

Pretty simple question: how do I sum over multiple indices that can only take specific values all together? To clarify: let's say I have the following sum: $\sum p_{a,b,c} f(a,b,c)$ where $f$ is a ...
1
vote
1answer
55 views

Solve for a variable using expression involving sum of quantities

I am trying to solve for h1 using function solve as in below code, Expression in solve equates sum of two expression. Both left hand and right hand side of expression is the sum of four quantities ...
2
votes
1answer
40 views

Indeterminant expression encountered in Summation

I have a function that I'm trying to find an explicit form for the coefficients in its power series expansion. On paper, it is a long calculation so I decided to write up the formula in mathematica. ...
1
vote
1answer
53 views

Summation notation

I have the current setup for calculating Allan Deviation: which was coded as: Sqrt[Total[Differences[y]^2]/(2 (M - 1))] However, after doing some research, ...
1
vote
1answer
85 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
votes
0answers
54 views

Iteration variable in Sum gets assigned the final iteration value

I've got a function which is defined iteratively via ...
1
vote
1answer
40 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
vote
1answer
86 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
votes
1answer
41 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 ...
0
votes
0answers
52 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 ...
0
votes
1answer
63 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
votes
1answer
68 views

Error from Compile with a sum over two indices

I have the following code: ...
2
votes
1answer
133 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
votes
2answers
230 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 ...
1
vote
0answers
90 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
65 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
vote
2answers
116 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
votes
1answer
118 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
votes
0answers
52 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
votes
1answer
39 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
vote
1answer
101 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, ...
1
vote
2answers
117 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 ...
7
votes
1answer
94 views

Sum over Binomials and Gammas

Given the function, ...
2
votes
2answers
172 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
votes
0answers
70 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
votes
1answer
53 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
vote
2answers
64 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 ...
1
vote
1answer
61 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 ...