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

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3answers
42 views

Can highlight an expression in mathematica in an expansion?

I ask mathematica to make an expansion of some expression. Is there a way to ask mathematica to highlight all terms that, say, goes by x^3 since it is really hard to find them? E.g. ...
2
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0answers
56 views

Ramanujan's asymptotic formula for $p(n)$

The following expression is the exact formula of partition function. Ramanujan's asymptotic formula for $p(n)$ is following $$p(n)\sim\frac{1}{4n \sqrt{3}}e^{\pi \sqrt{2n/3}}$$ Can I use ...
3
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0answers
74 views

Bug in Series[Pochhammer[1+n, n], {n,Infinity,1}]?

The function Pochhammer[1 + n, n] tends to infinity. We have ...
0
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0answers
28 views

Large exponentials in a series expansion [closed]

How can I get Mathematica to recognize that when I say Series[Exp[x]+1, {x, Infinity, 1}], I want to get Exp[x]? Or if this ...
3
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1answer
71 views

Find the function $f(x)$ by using its fourier expansion

It is easy to find the fourier coefficient and fourier expansion of $f(x)$ function. But I want solve the inverse problem by using Mathematica How to find the function $f(x)$, if I know its ...
2
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0answers
43 views

Unexpected imaginary term in the asymptotic expansion of DawsonF

FullSimplify[Series[2 DawsonF[x], {x, ∞, 8}]] (* -I Exp[-x^2] √π + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *) What is the reason the term ...
1
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1answer
28 views

`Series` acts on variables outside its argument?

I am trying to work with Taylor series. What I am trying to do is to express $$ f(h) - f'(0) = f(h) - f'(h - h) $$ such that only derivatives of $f$ with the argument $h$ appear, for example $$ f(h) - ...
3
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1answer
24 views

Asymptotics of Bessel function for real arguments

I am trying to calculate the following asymptotic behaviour: Normal@Series[BesselK[1, r \[CapitalLambda]] / BesselK[1, \[CapitalLambda]], {r, 0, 1}] but for ...
2
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1answer
61 views

Series expansions and algebraic branch points

I have the expression $$(1-x^4)^{-1/4}$$ where $0<x<1$, which gives me a real number. When I try to expand it around $x=1$, Mathematica gives me complex coefficients, which makes me think that ...
0
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2answers
93 views

Solving recursion relation from power series

I am interested in solving differential equations in the form of power series. Let's say we have following equation: $$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon ...
3
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0answers
67 views

A series in powers of $(a-z)$ instead of $(z-a)$

Sometimes it is more convenient to find a series expansion (e.g., Taylor, Laurent, Puiseux, ...) in powers of $(a-z)$ than in powers of $(z-a)$. For instance, the command ...
0
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0answers
52 views

break down the function

I am using Series function, but I found that it cost too much time. Since the Series function is Taylor expansion and I only need first order, I want to break down the code, so I can make it faster ...
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0answers
49 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 ...
1
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2answers
98 views
1
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1answer
113 views

Problem with solving a system of differential equations [closed]

I am trying to reproduce a result that is part of a derivation of the flow due to a rotating disk. I have as given this system of differential equations. (In these equations primes indicate ...
2
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3answers
129 views

How to write the Taylor expansion of the sum of several matrices?

When $A$ and $B$ are matrices, we have the following Taylor expansion for the inversion function together with basic information on convergence: $$ ...
8
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3answers
175 views

Expand series unevaluated

I'm newbie in Mathematica. I'd like to obtain nice and verbose output for any series calculation. For example, given a simple sequence n*(-1)^(n-1) and ...
2
votes
1answer
48 views

Getting rid of sub-exponential terms in an asymptotic expansion for a modified Bessel function

I am trying to get Mathematica to produce suitable asymptotic expansions for some modified Bessel functions at large argument (more specifically, the expansion in the DLMF's eq. (10.40.1)), and I'm ...
3
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0answers
75 views

How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
4
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1answer
147 views

Why does merely writing SeriesData[] with zeros give an error, even if it is never called?

Bug introduced in 8.0 or earlier and persisting through 10.4.1 Why does the code Function[t, SeriesData[t, 0, {0}, 0, 1, 1]] give me the following error? ...
0
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1answer
48 views

How to evaluate and simplify series expansions of long partial derivatives involving trigonometry?

I have 4 maps defined on a plane, i.e. on $\mathbb{R}^{2}$. Let's call them $F,G,H,J$. Let $(s,t) \in \mathbb{R}^{2}$. Define $F(s,t) = (f_{1}(s,t), f_{2}(s,t)).$ Likewise, in components, write $$ ...
0
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2answers
109 views

How do I get Series[] as a functional, rather than as an expression (i.e. to avoid the dummy variable)?

How can I write an equivalent to Series that doesn't require a dummy variable? Note that the series should be constructed before the evaluation point is supplied, ...
0
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0answers
70 views

Using Mathematica to derive an equation

My goal is to obtain Eq. (5) given in this Paper using Mathematica. First we need to define Eqs. (2) and (3) ...
2
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0answers
31 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
1
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2answers
59 views

How to expand an infinite product?

How can I use Mathematica to expand such a product (only need a finite number of terms): $$\prod^{\infty}_{n=1}\frac{({1-yq^{n+1}})({1-y^{-1}q^n})}{(1-q^n)^2}$$
4
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1answer
112 views

Successive Series Expansion Bug (?)

I've found what appears to be a bug in MMA related to taking successive series expansions. I'm providing this minimal example and post as other posts didn't appear to address the issue I found. In ...
1
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1answer
30 views

Multivariables series expansion up to some power of all the variables [duplicate]

I have a function f[x, y, z] that I would like to expand up to a given power of xyz. For now, I am using ...
0
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1answer
80 views

How can I calculate the root of any order of power series

How can I calculate the root of any order of power series with Mathematica. Here I insert every quantity by hand. But I want to give a, ...
1
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2answers
66 views

Engel expansion

How do I do an Engel expansion in Mathematica? And find the unique non-decreasing sequence of positive integers $ \{ a_1 ,a_2,a_3,\dots \}$ , such $$\frac{e}{\pi}=\frac{1}{a_1}+\frac{1}{a_1 ...
2
votes
2answers
116 views

Easier way to calculate Taylor remainder in 2nd order series

At the moment I have implemented the code for a Taylor 2nd order series for the function in three variables: $x_3^3+\frac{x_1-x_2}{x_1+x_2}$ The code builds on following expression: ...
5
votes
2answers
134 views

Power series expansion

I am asking Mathematica for the first 5 terms in a power series expansion like this: ...
-1
votes
1answer
62 views

Taylor and Maclaurin series [closed]

I need to calculate limit of sin(x)*cot(tanx) at 0 using Maclaurin series I took the usual approach but did not get anything of help.
3
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1answer
70 views

SolveAlways 'never' completes

After allowing Mathematica to run on ...
5
votes
5answers
157 views

How to find the derivative value at $(\pi,0)$ for this implicit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
6
votes
1answer
192 views

Trouble with shooting method for a 4th-order differential equation

I'm trying to solve the following forth-order ODE with the shooting method: $$\frac{1}{5}(y-2xy^\prime)=\frac{1}{x}\left\{\frac{xy^\prime}{y}+xy^3 \left[\frac{(xy^\prime)^\prime}{x} \right]^\prime ...
4
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2answers
225 views

Chebyshev Approximation

Is there functionality in Mathematica to expand a function into a series with Chebyshev polynomials? The Series function only approximates with Taylor series.
0
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1answer
74 views

Series expansion not possible for more than two variables?

My problem is simple. I want to evaluate the series Series[(1 + x*b - x*a)/(1 + 2*x*c - 2*x*a), {a, 0, 2}, {b, 0, 2}, {c, 0, 2}]. Mathematica output looks like ...
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1answer
137 views

I was wondering how to get the following result by mathematica or maple or other way [closed]

[![enter image description here][1]][1] I was wondering how to get the following result by mathematica or maple or other way I have asked this question several days ago and recently I have got some ...
0
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2answers
73 views

plotting summation to check for convergence

Our assignment was to enter in a series and check to see if it converges by graphing. However, when I attempt to graph it, I get a bunch of errors that I'm not sure what they mean. Best way to show ...
5
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0answers
79 views

Getting around Series[Sinc] bug

For some reason, Series expansion of Sinc around x=0 for low orders fails to generate a ...
1
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3answers
102 views

How to find the leading term in the expansion for large value of the parameter

My question is related to one I already asked (previous question). The equation I am working with is cumbersome: ...
4
votes
1answer
66 views

series to rational order

The function Series requires that the expansion order is an integer, i.e. for the input ...
1
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1answer
92 views

Problem with complex conjugation of series data in mathematica 10

ComplexExpand in Mathematica 10 doesn't work with series data: Taylor = Series[Exp[I x], {x, 0, 4}]; ComplexExpand[Taylor\[Conjugate]] gives 1+I x-x^2/2-(I ...
1
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2answers
126 views

Solve of cubic and quartic equations too slow

In my problem I have a third order algebraic equation for the variable sigma, all other letters are parameters. Here is it's right-hand side, left hand side is ...
1
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0answers
69 views

Finding consecutive residues of large expression?

I have given a large expression expr (has LeafCount of 2772, you can find it in this file or ...
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votes
2answers
121 views

How to create a series using For loop.? [closed]

i want to create a series such as 10^n-1 * 10^n-2 *.......... * 10^2 * 10^1 using for loop ; here is my code. For[n=1, n<18, a=10^n; n++, b=(10^n)*a;]; ...
1
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5answers
190 views

Getting $e$ closer than $0,001$?

Everyone knows that $\sum \frac{1}{n!} =e$. How should I make a program in Wolfram Mathematica, that tells me, how many members I need from the sum, to get a number, with mistake smaller, than ...
2
votes
1answer
93 views

Finding terms of the perturbation solution

I've got a task to find first three terms of the perturbation series solution to: $$y' = 1 +(1+\epsilon)y^2,\quad y(0)=1, \quad t > 0,$$ for a small $\epsilon$. I am supposed to use Mathematica ...
1
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1answer
70 views

Series around a point

I have the function Vt ...
2
votes
1answer
64 views

Solving ODE in power series about infinity

I want to solve a particular ODE in power series of 1/x. I can obtain the power series solution about x=0. Can any one suggest how to obtain a series solution in 1/x for the following ODE? I tried ...