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

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0
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0answers
11 views

How to deduce the Ramanujan's summation of this series?

I have already asked a similar question about Ramanujan's summation in general but received no good answers. Now I am interested in this exact series: $$\sum _{n\ge1}^\Re (24 n + 12 n^2)$$
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
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 ...
-1
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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 ...
4
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4answers
243 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 ...
2
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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 ...
11
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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 ...
4
votes
2answers
170 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 ...
8
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4answers
231 views

Is it possible to find generating functions of infinite sequences with Mathematica?

I'm trying to find the generating function of a sequence as $(0,1,0,1,0,1,\dots)$ but reading Mathematica's help on FindGeneratingFunction[] seems to tell me that ...
3
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3answers
468 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 ...
4
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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 ...
9
votes
4answers
1k views

Ways to compute inner products of tensors

One way to evaluate the following sums is combining Table and Sum: $u_{abcd} = \sum_{e=1}^3 v_{aeb}w_{ced}$ $q_{ab} = \sum_{d,e=1}^3 v_{d e a}w_{deb}$ It will look like ...
1
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1answer
86 views
1
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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 ...
2
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1answer
194 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
9
votes
1answer
121 views

Bug in GeneratingFunction?

Bug introduced in 7.0 and fixed in 9.0.0 According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I ...
3
votes
1answer
342 views

Summation of If statements

The following made me curious. Suppose you want to sum the if statement If[x[i] < 1., x[i]^2, 0.] over i=1,2, i.e. ...
3
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3answers
492 views

Efficiently compute double sum

Is there a "Mathematica Way", like Map or Apply to compute the following double sum? $\sum_{i=1}^{N_1}\sum_{j=1}^{N_2} m_i n_j \, f(\tau_{i} \gamma_{j})$ I have already stored the lists ...
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 ...
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
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1answer
85 views

Simplify a huge expression with limited memory

I would like to perform some analytical sums such as the following ...
1
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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.
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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
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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; ...
10
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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 ...
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
1answer
204 views

How to calculate the unknown quantity in an infinite series?

I'd like to calculate x value in this equation. Basically, I tried to 2 types of method which are FindRoot and NSolve. But, I have failed the calculation caused by these errors up to now. If ...
0
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1answer
273 views
11
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3answers
377 views
0
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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
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1answer
57 views

Weird sum regularization? [duplicate]

I noticed some weird behavior in "Dirichlet" regularization of infinite sums. Let us first compute ...
1
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0answers
103 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...
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
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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
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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
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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, ...
0
votes
1answer
118 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 ...
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 ...
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: ...
1
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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 ...
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 ...
9
votes
2answers
235 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 ...
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 ...