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

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2
votes
2answers
314 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 ...
7
votes
0answers
192 views

Incorrect evaluation for Thue-Morse signed harmonic series

I would like to evaluate $$s = 1 - \frac{1}{2} - \frac{1}{3} + \frac{1}{4} - \frac{1}{5} + \frac{1}{6}+\frac{1}{7}-\frac{1}{8} - ... + \frac{(-1)^{\textrm{binary digit sum}(n-1)}}{n} + ... $$ where ...
6
votes
0answers
75 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 ...
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 ...
4
votes
0answers
67 views

Can a single Sum with multiple iterators be different from nested Sums?

Multiple sums are documented with two or more iterators, for example: Sum[1/(j^2 (i + 1)^2), {i, 1, Infinity}, {j, 1, i}] however the same answer can be ...
4
votes
0answers
108 views

Multiple Constrained Sum

I need to perform a multiple summation, that obeys some conditions. This arises in the study of a statistical physics model. q=Exp[-β]. I would like to ask if ...
3
votes
0answers
91 views

How to get this terrible summation/product to run in Mathematica?

I've come across this formula and have no idea where to even start. (My assumption here is that $m,n$ are known and input into the expression to arrive at an answer.) $$f(m,n) = \sum_{\substack{0 \...
2
votes
0answers
61 views

Why can Mathematica compute numerical sums more efficiently when they are written as matrix operations?

Let $f(n)$ and $K(n,m)$ be functions such that the double sum, which we wish to evaluate numerically, $$ \sum_{n=1}^a \sum_{m=1}^a f(n) f(m) K(n,m) $$ exists when $a$ is some large positive number. I ...
2
votes
0answers
61 views

Follow-up to “How to differentiate formally?”: Efficiency concern

In link to "how to differentiate formally?" and particularly to the answer by @Jens, I want to do something like this: ...
2
votes
0answers
148 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 $x_{i_j}$ ...
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 ...
2
votes
0answers
252 views

Computing a sum

I'm trying to make Mathematica compute this sum: Sum[(-1)^k (n - k)^2 Binomial[2 n, k], {k, 0, n}] As is, I get an awful formula: ...
2
votes
0answers
281 views

Faster Ways to compute recursive summation

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
2
votes
0answers
84 views

Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity]

I would like to show that the following (and other similar formulae) tends to zero. Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity] What's the right ...
1
vote
0answers
27 views

Partial Sum of Binary Sequence not Working

I have the following code: ...
1
vote
0answers
61 views

Assumptions aren't working in this sum

I have a sum that should be real: FullSimplify@Sum[1/(α n^4 + β), {n, 1, ∞}, Assumptions -> α > 0 && β > 0] But the result have involved even ...
1
vote
0answers
47 views
1
vote
0answers
74 views

Problem with calculating Harmonic Numbers

I have tried to take a series of Harmonic Numbers using mathematica but there have been issues in calculations. So far when I computed the sums at a small value range such as ...
1
vote
0answers
63 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
90 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; ...
1
vote
0answers
100 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 ...
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
0answers
113 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
0answers
97 views

How to evaluate sums that have 0^0 = 1

In my code: ...
1
vote
0answers
79 views

Summing a trig series

I am trying to sum the following expression: (Cos[(2 π m)/N]^2 Cos[(2 π n)/ N])/(2 (Cos[(2 m π)/N] - Cos[(2 n π)/N])) from m=1...
1
vote
0answers
96 views

Manipulating infinite series

If I type Sum[f[x],{x,m,Infinity}]-Sum[f[x],{x,m+3,Infinity}] I would like Mathematica to return something like ...
0
votes
0answers
51 views

Symbolic series

Mathematica realises, of course, how to deal with symbolic series: Sum[g[x]^k, {k, 0, ∞}] (*Out: 1/(1 - g[x]) *) I.e. it does not worry about values of ...
0
votes
0answers
35 views

Creating a non-zeta-ified sum

The expression Sum[i^(-s), {i, 1, ∞}] evaluates to Zeta[s] But, of course, this is not strictly correct as ...
0
votes
0answers
36 views

Problem of Summation

I want to calculate something like this: $$w_t = \sum_{i+j=t}c_{5-i,4-j}.$$ for $t=0,1\cdots8$. How I can write the code? I assume that $i$, $j$ and $t$ are all positive integers. Thank you very ...
0
votes
0answers
60 views

Sum of Infinite convergent series

I have a series as Sum[(x^1 - (x - 1)^1) (b^Log[(1 + (x))]), {x, 1, Infinity}] which is convergent when b=0.3 and ...
0
votes
0answers
31 views

Simplify expression?

Suppose I have expressions that involve terms like: p1.p1+p2.p2+p3.p3+p4.p4 p1, p2, p3, and p4 are all elements of an array: ...
0
votes
0answers
58 views

Extract coefficients from sum

I would like to extract coefficients of indexed variables from a large sum. The following is an example motivated by linear regression to illustrate the problem. Consider the (unnormalised) log ...
0
votes
0answers
284 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 <...
0
votes
0answers
46 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 ...
0
votes
0answers
58 views

More on performance of Sum[]

There is an interesting discussion on performance of Sum[] in this question. I actually wanted to reproduce findings from this answer. So, I entered: ...