Questions on dealing with series data and constructing power series expansions of functions.

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27 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: Sum[x[n], {n, 1, 1 + m}] - Sum[x[n], {n, 1, m}] it returns ...
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1answer
53 views

to find limiting value of function at large N i.e. N->infinity

Is it possible to find the limiting value of function at large N ...
0
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1answer
37 views

How to turn arbitrary function to polinomial series in Mathematica?

Can I turn any multivariate function into polinomial series in Mathematica? Suppose I have a function Fwd[x_, α_] := x (1/Sin[Pi x/2])^α and wish to express it ...
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0answers
16 views

Infinite series [migrated]

Good afternoon. I'm brazilian, then sorry by my bad english. I have a problem with one question about Infinite Series. I searched for anyone method could help me. I have all constants values (w, y, ...
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0answers
48 views

to determine asymptotic value of function when N->infinity [on hold]

To determine the asymptotic value of function for large value of N, given 'm' is much less than N i.e. in the limit N->infinity and m/N->0 $f(m,N)=\sum_{a=1}^{\lfloor N/2 \rfloor} \binom{N}{S} ...
6
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2answers
163 views

How to reverse irreversible function in Mathematica?

How to reverse formula $y(x)=x (\frac{1}{sin \frac{\pi x}{2}})^\alpha$ i.e. express it as $x = x(y)$ in Mathematica? I did this way ...
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0answers
26 views

Don't understand Series expansion in my scope

I have a quite complex, implicit problem where I have the following (short version): ...
0
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0answers
25 views

FourierSinCoefficients extremely slow

I'm just playing with Fourier decomposition of periodic functions. We had a similar example with standing waves and cosines in class, so I tried to expand a triangle wave in sines. This is what I came ...
5
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0answers
93 views

Contour Integration along a contour containing two branch points

I need to compute following contour integrations: $$f(u)=\oint_\alpha dz \sqrt{z^3+z+u} \qquad ; \qquad g(u)=\oint_\beta dz \sqrt{z^3+z+u}$$ In which $\alpha$ and $\beta$ are two contours in ...
2
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1answer
69 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
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0answers
23 views

power series or taylor series for transcendental equation [closed]

Can anyone please show me how to find a power series or taylor series for $p(h)$, an implicit function of $h$ implied by the following equation: $-plog(p) - (1-p)log(\frac{1-p}{n-1}) - h = 0$ ?? ...
0
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1answer
58 views

Series with a specified number of terms

I'm doing calculations with Series where I don't know the power of the leading order term. I would like to keep a specified number of terms, but since I don't know the leading order this is proving ...
16
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4answers
375 views

Expansion of a hypergeometric function takes ages with Mathematica 9 and 10 (regression?)

Mathematica 8 (Linux version) can evaluate AbsoluteTiming[Series[Hypergeometric2F1[1, 1 - eps/2, 3 - eps, 1/2], {eps, 0, 0}]] in no time. On one of the ...
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1answer
65 views
0
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1answer
71 views

How to obtain Laurent series coefficients of an (almost) arbitrary function?

I have observed that Series in Mathematica assumes that the given function is smooth in the point around which one wants to perform series expansion. For instance: ...
2
votes
4answers
88 views

Extract a part of Series

If I have the output of Series, in terms of powers of my variable $x$, what is the quickest way to extract a part of the series, say for example the terms from $x^2$ to $x^5$, excluding those with ...
0
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1answer
25 views

Extract a term of `Series` output

Say I have the output of series, with all the coefficients of the different powers of my variable $x$. What is the quickest way of extracting the coefficient of the $n$-th power of $x$?
1
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1answer
37 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 ...
0
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1answer
46 views

Series identity with binomial coefficients [duplicate]

I have this apparently simple equation: ...
2
votes
2answers
75 views

Series expression of a Root object

I was wondering if it is possible to get Mathematica to return a series approximation of a Root object. Example: I want a series representation of x in terms of ...
1
vote
2answers
113 views

Linearization of differential equations

I was wondering if one could define an operator such that, when I give a certain number of (differential) equations as an output, and an "equilibrium" value for each of the variables, it returns the ...
0
votes
1answer
64 views

Can't get solution to a system of recurrence equeations

I would be grateful if someone could help me with this problem. I define two series recursively, thus: ...
5
votes
5answers
124 views

Isolating cross terms

I have a set of expressions that contains terms like $\frac{1}{(x + a + b)(c+d)}$. I would like to simplify the denominator so that products of $a,b,c,d$ are dropped, but $x c$ and $x d$ are kept. ...
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0answers
52 views

Linearization of differential equation - need tips for the use of Series function

I would like to linearize a differential equation around a equilibrium position. The description of the steps that I have carried out are : Equation ...
3
votes
1answer
144 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
7
votes
1answer
227 views

Error in infinite sum

The binary weight of the non negative integer k is defined by w[k_] := Total[IntegerDigits[k, 2]] The first values are (cf. http://oeis.org/ A000120) ...
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2answers
36 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 ...
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1answer
33 views

Derivative inside a Series [closed]

I have a function defined by a sum, which I would like to differentiate. For example: ...
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1answer
49 views

Don't understand why my Taylor expansion results in a message and an unexpected result

Trying to do something simple: Taylor expand a generic function of t around a point t and substitute ...
5
votes
2answers
86 views

Replace expression in series expansion [duplicate]

A test case: I'm trying to replace an expression inside a series expansion: Series[f[x],{x,x0,4}] ./ (x-x0)->h but it still returns ...
0
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0answers
103 views

Alternative to Series

Here is a sample of my code: ...
0
votes
1answer
81 views

Series expand root of quartic polynomial containing many real parameters and FullSimplify return `Indeterminate`

Using Mathematica I can get the Eigenvalues of the following matrix (using Quartics->True): ...
0
votes
1answer
45 views

Series expansion of large expression

I have the following equation: eq=E0[x,y,z]+E1[x,y,z]*Cos[phi]+E2[x,y,z]*Cos[phi]^2+E3[x,y,z]*Sin[phi] Now E0,E1,E2 and ...
0
votes
1answer
71 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
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0answers
31 views

SumConvergence with product $\sum_1^\infty{\frac{1\times3\times5\times…\times(2n-1)}{n!}}$

SumConvergence[( Product[(2 n - 1), {n, 1, infinity}])/n!, n] $$\sum_1^\infty{\frac{1\times3\times5\times...\times(2n-1)}{n!}}$$ However this returns true but it ...
0
votes
2answers
57 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
2answers
77 views

Series with specific notation

I'm trying to get mathematicas series function to output a result that look like this: instead of calculating the actual "values", like doing so here: ...
2
votes
3answers
252 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. ...
1
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1answer
37 views

Series power with unusual denominator

I have a series whose terms are: (x^n)/(n+a) where n is a positive integer, x a real number that is greater than 0 and smaller than 1, and a is a real number smaller than 1. It is easy to proof that ...
3
votes
1answer
37 views

Defining the value of variable after expansion

I have an initial equation defined as: x = Subscript[a, 0] + (1 - r^2)/Sqrt[1 + r^2 - 2*r*Cos[\[Theta]]]; I want to taylor expand this after subbing in: ...
3
votes
1answer
105 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
0
votes
1answer
79 views

How to obtain Padé approximant of $\log(x)$? [closed]

Having read this answer on Math.SE, I wanted to try seeing how Padé approximations converge to $\log(x)$. But my first attempt after reading the documentation failed: ...
0
votes
1answer
58 views

Single formula for this sequence [closed]

Consider the following sequence. 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8 We can express this sequence by (an) where an=n/2 when n is even and an=0 when n is odd. Find a single formula for an ...
4
votes
3answers
208 views

Polynomial with alternating sign coefficients from the odd degree terms of a Truncated Power Series

I'm trying to make a function that will take any truncated power series I give it, strip away all the even degree terms, then change the sign of the coefficients of every other term. So that we have a ...
2
votes
1answer
98 views

Evaluate function defined by DifferentialRoot

I have the following sequence of rationals that I want to find the generating function of: ...
4
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1answer
152 views

How do I find a series solution for $$e^{-\frac{1}{2}f'(x)} cosh( f(x) ) = ax + b$$

I am trying to approximate a function $f(x)$ satisfying a relation between $f(x)$ and its first derivative. How do I find a series solution for $$e^{-\frac{1}{2}f'(x)} cosh( f(x) ) = ax + ...
1
vote
1answer
80 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
14
votes
1answer
252 views

Why do big-O terms disappear in definite integrals since Mathematica 9?

In Mathematica 8, when I computed the following input: Integrate[Series[Cos[x], {x, 0, 2}], {x, 0, a}] Mathematica returned an expression that had a O[a^4] in ...
4
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0answers
56 views

FindSequenceFunction for sum of hypergeometric terms

Mathematica's built-in function FindSequenceFunction is quite good at recognizing hypergeometric terms, i.e. terms $c_k$ for which $c_{k+1}/c_k$ is a rational ...
3
votes
1answer
118 views

Problem with series expansion and integrate

I have the following very simple code. A power series in a-parameter, function f[x], is integrated with respect to x, and the ...