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

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1answer
173 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
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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
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2answers
71 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
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1answer
141 views

How to rewrite and possibly speed up a recursive sum?

I have the following for-loop calculating a multiple nested sum ...
1
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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 ...
2
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3answers
134 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
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3answers
431 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
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2answers
111 views

Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
1
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1answer
186 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
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1answer
186 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: $$\sum_{i_1+i_2+...+i_n=k}\binom{k}{i_1,i_2,...,i_n}\frac{f(...
3
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3answers
828 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 $$\sum_{i_1+i_2+...+i_n=...
8
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4answers
274 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 ...
1
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1answer
224 views

Summand is not numerical at some point

I am trying to do some numerical integration with the following codes: ...
0
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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 ...
1
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2answers
112 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
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1answer
98 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
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3answers
138 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
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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 \...
3
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5answers
164 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
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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: ...
1
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2answers
231 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), j=(...
5
votes
3answers
288 views

The speed of Sum[] varies strangely

I was curious about the difference in speed between Total and Sum. I found out Total was ...
4
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3answers
593 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} f(j)...
1
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2answers
159 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
183 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 Sum}[S_i\,...
1
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1answer
732 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
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2answers
192 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
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1answer
96 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
157 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 _{n=1}...
5
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1answer
294 views

Compile nested Sums

I want to compile an expressions that contains nested Sum-expressions. A simple example that gives me problems is: ...
7
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1answer
414 views

Understanding Dirichlet regularization in Sum

I've tried to calculate few classic sums using Dirichlet regularization: ...
8
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2answers
249 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
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0answers
97 views

How to evaluate sums that have 0^0 = 1

In my code: ...
1
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1answer
145 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
717 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
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2answers
138 views

Collapsing summation

I am trying to write a command to collapse the sum of terms into an expression with summation. Something like ...
17
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3answers
332 views

sudden increase in timing when summing over 250 entries

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 instance, this table contains sums ...
1
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1answer
155 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
180 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
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1answer
277 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 ...
0
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1answer
251 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 there ...
1
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2answers
134 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 ...
2
votes
1answer
396 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 didn'...
3
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1answer
224 views

Collect terms in a sum

Suppose I have this expression ...
0
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2answers
101 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) = ...
2
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1answer
257 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] = \frac{(N\bar{x}...
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 ...
4
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1answer
81 views

Strange NSum behavior for slightly larger number of terms

For some sums, NSum gives me the result nicely for some number of terms, but if I add one more term, it suddenly becomes much slower. I haven't found the minimum example for which this can be ...
12
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7answers
737 views

Numerical evaluation of a sum

I am trying to compute numerically NSum[(-1)^n/n^3, {n, 1, Infinity}]. Of course, using first Sum would work here, but often it'...
3
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1answer
577 views

How can I speed up this code with multiple sum?

There are 4 variables in this multiple sum, therefore it may take a long time. I have run this program for 12 hours, but no result untill now. I want to know how to speed up this code. Any help or ...