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

learn more… | top users | synonyms

1
vote
0answers
88 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
81 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
92 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
80 views

Weird sum regularization? [duplicate]

I noticed some weird behavior in "Dirichlet" regularization of infinite sums. Let us first compute ...
10
votes
2answers
327 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 Limit[n*Sum[...
1
vote
1answer
83 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
103 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
150 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
97 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
46 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
123 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
137 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
58 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 series?...
1
vote
1answer
115 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
64 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
73 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
91 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
88 views

Error from Compile with a sum over two indices

I have the following code: ...
1
vote
1answer
81 views

Subtracting Series

When I input the following $$\sum_{n=0}^{m+1}x[n]-\sum_{n=0}^{m}x[n]$$ which in InputForm is: ...
2
votes
1answer
179 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
votes
2answers
294 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
98 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
81 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
151 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
193 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
141 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
53 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
115 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
149 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
117 views

Sum over Binomials and Gammas

Given the function, ...
2
votes
2answers
198 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
83 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
65 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
101 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
99 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
votes
1answer
515 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} \end{align}...
1
vote
0answers
83 views

FullSimplify missing trivial rewrite

I'm trying to understand why Mathematica fails to find the Stirling numbers in the second sum below: ...
1
vote
2answers
39 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
votes
1answer
79 views

Derivative inside a Series [closed]

I have a function defined by a sum, which I would like to differentiate. For example: ...
2
votes
0answers
45 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 ...
0
votes
1answer
48 views

Summation of functions [closed]

I want to define a function that is a sum of other functions. For this, I define functions of the form ...
0
votes
0answers
281 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
309 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 $$A_{i}A_{...
6
votes
4answers
277 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
votes
0answers
64 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
votes
1answer
162 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 f(x)\,{\mathrm{...
0
votes
2answers
77 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
votes
2answers
68 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
vote
1answer
139 views

How to rewrite and possibly speed up a recursive sum?

I have the following for-loop calculating a multiple nested sum ...
1
vote
1answer
100 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 ...