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5
votes
0answers
45 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
30 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 ...
0
votes
0answers
42 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 ...
0
votes
0answers
24 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
50 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
59 views

How to rewrite and possibly speed up a recursive sum?

I have the following for-loop calculating a multiple nested sum ...
0
votes
0answers
52 views

How to implement Ramanujan's summation of divergent series in Mathematica? [closed]

How to implement the Ramanujan's method of summation of divergent series in Mathematica?
1
vote
1answer
58 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
112 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
votes
3answers
214 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
88 views

Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
1
vote
1answer
121 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
votes
1answer
68 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
vote
2answers
212 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
86 views

Summand is not numerical at some point

I am trying to do some numerical integration with the following codes: ...
0
votes
0answers
41 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 ...
1
vote
2answers
71 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 ...
0
votes
1answer
29 views

Error with numerical summation - how to specify “n choose r”?

I'm trying to do the following sum: NSum[((50000 - x) choose x)*(1/3^15)^x*((3^15 - x)/3^15)^(50000 - x), {x, 1, 4}] But I keep getting an error saying: ...
0
votes
3answers
65 views

how to remove the divergent term from the summation?

I am doing the summation over two indices: m and n Suppose I want to remove those terms from the summation which has m==n, what ...
1
vote
0answers
76 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 ...
3
votes
5answers
110 views

Symbolic versus numeric sum (is there an inconsistency?)

Something seems to have gone awry with the analytic sum (v9.0.1). Here I insert specific values: ...
0
votes
0answers
47 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: ...
0
votes
2answers
44 views

Dynamic nested sum

I would like to dynamically create nested sums with a dynamic number of parameters aswell. We do know the number of variables. Lets say we have 3 Variables with S being an array: $$ i=(1,\dots,m), ...
5
votes
3answers
242 views

The speed of Sum[] varies strangely

I was curious about the difference in speed between Total and Sum. I found out Total was ...
2
votes
3answers
123 views

Skip certain values in a sum

How can I evaluate such a sum: $$ \sum_{j=0, j\neq10}^{J} f(j) $$ Since I am trying to do some symbolic calculations, solutions such as the one below are undesirable: $$ -f(10) + \sum_{j=0}^{J} ...
1
vote
2answers
34 views

Summing over n variables [duplicate]

I am currently trying to create a function taht will sum over n variables, but I don't really know how ot implement it. It should look like this: $f[n]=\left(\frac{1}{6}\right)^n \sum _{x_1=1}^6\sum ...
5
votes
3answers
149 views

Can I regroup terms into a sum?

Is there a way to regroup terms into a sum? I mean, for example, if I have the sequence $\quad \quad S_1 S_2 + S_2 S_3 + S_3 S_4 + S_4 S_5$ I would like to get the form $\quad \quad {\rm ...
1
vote
1answer
104 views

Derivative of an expression containing a symbolic sum [duplicate]

Is there a general pattern for working with symbolic sums in Mathematica? For example here's a derivative I want to compute: ...
5
votes
2answers
75 views

Simplification due to recognition of dummy indices in sums?

Today I noticed something weird concerning implicit sums. Apparently, Mathematica cannot recognize dummy indices as such and simplify accordingly. Consider: ...
3
votes
1answer
66 views

Leave out a term when summing

I'm calculating the Madelung constant $$\alpha = -\sum_{n_1,n_2,n_3}{\frac{(-1)^{n_1+n_2+n_3}}{(n_1^2+n_2^2+n_3^2)^{1/2}}}$$ Where $n_1,n_2,n_3$ are any element in the integer domain and they can't ...
3
votes
1answer
125 views

How do I format Compile[] correctly?

My Mathematica skill is still rusty, so kindly bear with me. I'm having problem formatting expression to compile the function correctly: $\sum _{g=1}^G \sum ...
5
votes
1answer
130 views

Compile nested Sums

I want to compile an expressions that contains nested Sum-expressions. A simple example that gives me problems is: ...
5
votes
1answer
113 views

Understanding Dirichlet regularization in Sum

I've tried to calculate few classic sums using Dirichlet regularization: ...
8
votes
2answers
182 views

Error computing sum of sum of digits

I've defined a function that computes the sum of the base-b digits of n: DigitSum[n_, b_] := Total[IntegerDigits[n, b]] Then I defined a function that computes ...
1
vote
0answers
76 views

How to evaluate sums that have 0^0 = 1

In my code: ...
1
vote
1answer
69 views

How to factorise a variable out of an indefinite sum?

(I should start by saying I'm a total beginner with Mathematica, so if the answer needs code I'll need it spelled out quite clearly, the learning curve for this is proving steep!) Basically what I am ...
2
votes
3answers
349 views

Sum with Levi-Civita [duplicate]

I'm trying to write the expression $$\sum_{\alpha,\beta = 1}^{4}\epsilon_{\mu \nu\alpha\beta}a^{\nu} b^{\alpha} c^{\beta}$$ in Mathematica, where $\epsilon$ is the Levi-Civita symbol and $a$, $b$, $c$ ...
0
votes
2answers
100 views

Collapsing summation

I am trying to write a command to collapse the sum of terms into an expression with summation. Something like ...
9
votes
2answers
186 views

sudden increase in timing when summing over 250 entries

Using math 9.0.1 on a MacBook Air, I see a sudden increase of Timing by a factor of thousands when I sum over 250 elements of a matrix rather than over 249. So for ...
1
vote
1answer
69 views

How would one minimize with respect to an unknown number of variables?

Say I had a function like the following: f[n_] := Sum[a + Subscript[b, k], {k, 0, n}] Such that ...
0
votes
2answers
93 views

How can I speed up this code?

There are 4 variables in this multiple sum, and only 2 are used. This question has the similar scenario as the previous one How can I speed up this code with multiple sum?, but the calculation ...
2
votes
1answer
162 views

Problem with infinite sum

I am facing a problem in evaluating infinite sums of the following form. As a first thing define the following function ...
1
vote
2answers
96 views

Problem evaluating a complicated integral

Apologies for stating my problem poorly in the first instance, thank you for the help in narrowing down the issue. Problem For those interested, it's for the exact unbiased inverse of the ...
1
vote
1answer
128 views

Symbolic evaluation of the sum of KroneckerDelta

I want to evaluate this simple expression $$ \sum_n f(n)\delta_{mn} = f(m) $$ using this: Sum[KroneckerDelta[m, n] f[n], {n, Infinity}] However Mathematica ...
0
votes
0answers
30 views

How to calculate this derivative? [duplicate]

Can Mathematica do the following simple calculation? $$F(x_0, x_1, x_2, ...) \equiv \sum_n x_n^2$$ I want to do the symbolic calculation: $$ \frac{\partial F}{\partial x_m} = \sum_n 2 x_n ...
3
votes
1answer
118 views

Collect terms in a sum

Suppose I have this expression ...
0
votes
2answers
90 views

How do I sum up p items in a sequence?

I have the following sequence list = {p1, p2, p3, p4 ....} I am summing up the p items as follows: p1 + p2 + 2*sqrt (p21*p2) = p12 p12 + p3 + 2*sqrt (p12*p3) = p123 p123 + p4 + 2*sqrt (p123*p4) = ...
0
votes
0answers
54 views

Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
2
votes
1answer
130 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
1
vote
1answer
119 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 ...