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Questions tagged [series-expansion]

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

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How to Series Expand an Expression in Mathematica with Smaller Cross Terms Compared to Diagonal Terms?

I have an expression for E_y in terms of various s terms, and I want to perform a series expansion based on the assumption that cross terms (like s12) are much smaller than the diagonal terms (like ...
ions me's user avatar
  • 1,023
0 votes
1 answer
67 views

Finding a sequence function

I would appreciate your help in finding a polynomial sequence function based on a set of data points. For each pair of integers {j, k}, I have the following data points ...
Hawi's user avatar
  • 173
2 votes
2 answers
162 views

Incomplete Series Evaluation in Mathematica for Large Values of 𝑛

The evaluation of the series Series[((1/2 + Sqrt[n])^3 n^(15))/(((7 Sqrt[2])/(3 n^(1/4)) + C1/n^(3/4) + n^(1/4))^(37)), {n, Infinity, 2}] Does not complete where ...
Lorenz H Menke's user avatar
2 votes
2 answers
102 views

Series expansion not working with $\sqrt{1-x^d}$

Why can't Mathematica expand simple functions like $$\sqrt{1-x^d}$$ in series? When I give particular values of $d$, then it simplifies but not otherwise. For now, I want $d \in \mathbb{N}$, and want ...
Sanjana's user avatar
  • 195
0 votes
1 answer
50 views

Find radius of convergence for two series product [closed]

I have a equation like this: (u + v + w + 2 u w + 2 v w + 2u v + 3u v w)/[1 - (v w + uv + uw + 2 u v w)] ...
Ama's user avatar
  • 21
1 vote
1 answer
38 views

Getting coefficients list of a series expansion at a point different from 0

I would like to get the coefficients of a series expansion at a point different from 0. Example: Series[Cos[Pi*x], {x,1,6}] which gives $-1+\frac{1}{2} \pi ^2 (x-...
edrezen's user avatar
  • 113
2 votes
2 answers
260 views

Series expansion of a given function

I attempt to do the series expansion for the following function ...
Vayne's user avatar
  • 101
1 vote
0 answers
49 views

Use Series[] using noncommutative multiplication

Let's consider Newton's method for systems of nonlinear equations $$y^{(k)}=x^{(k)}-[F'(x^{(k)}]^{-1}F(x^{(k)}).$$ And I want to use Taylor series for the above method. So considering that $$F( x^{(k)}...
Alejandra Benítez's user avatar
1 vote
0 answers
57 views

Replacement rule runs for a long time [duplicate]

I have a simple expression that reads (some expression in b) q^(8/3): ...
Lelouch's user avatar
  • 543
1 vote
0 answers
78 views

Simplification of expression with PolyLog[4,2]

I am trying to simplify the following expression. expr=1/2 \[Pi]^2 Log[2]^2-2/3 I \[Pi] Log[2]^3-4 PolyLog[4,2]+7/2 Log[2] Zeta[3] This ...
BabaYaga's user avatar
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9 votes
1 answer
427 views

Calculating relative error of Ramanujan formula for ellipse perimeter

On this page, they present the Ramajujan's second formula for the perimeter of an ellipse: $$P \approx \pi (a+b) \left(1+ \frac{3 h}{\sqrt{4-3 h}+10}\right),$$ where $h=(a-b)^2/(a+b)^2$. They expand ...
Ytrewq's user avatar
  • 179
3 votes
3 answers
103 views

How to invert a series with two variables, where the series is expanded in the other variable?

I have defined an expression that is a series in powers of $1/c$: ...
Christopher's user avatar
1 vote
1 answer
53 views

Solving algebraic equations perturbatively (using function series)

I have linearised some equations and trying to solve them perturbatively in powers of small parameter $e$. Here is my script ...
Marco's user avatar
  • 163
1 vote
1 answer
78 views

The Baselproblem from Euler

$Zeta(2) = 1/6 Pi^2$ This is the value of the Riemann Zeta function "for the number 2 Euler the famous mathematician first calculated this symbolic value in the 18 century in his "Basel ...
janamdo's user avatar
  • 11
0 votes
1 answer
56 views

Convergent Taylor series unrecognized by Sum

I am trying to understand why Sum does not recognize a particular Taylor series as convergent. I have defined a function 'series' like this, that computes the Taylor series of a function 'f' at 'x', ...
Glenn Welch's user avatar
3 votes
1 answer
84 views

How to find the asymptotic envelope of a function?

Context I am interested in the asymptotic behaviour of the envelope of a given function. Unless I missed it, it would be of interest to have a Mathematica function which when given ...
chris's user avatar
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0 votes
0 answers
61 views

How to access the Wolfram Data Repository

How I can obtain the raw data of different epidemics in different viruses such as COVID-19, ebola, influenza, etc.? I consulted the site but I can't figure out how to extract the data in real time to ...
azo's user avatar
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1 vote
1 answer
48 views

Set the value of a parameter in a Series expression [closed]

I have a lengthy expression resulting from a series expansion in some dummy variable $e$ which I now wish to set equal to 1. However, when I try to use a ReplaceAll ...
Matthew Ward's user avatar
3 votes
1 answer
108 views

Asymptotic integral expansion at infinity [closed]

Define for all $n\in\mathbb{N}$, a definite double integral, $$I_n= \int_{0}^{1}\int_{0}^{1}\left(\frac{x^2(1-x)y^2(1-y)}{1+x^2 y^2}\right)^n\frac{\cos((2n+1)\tan^{-1}(xy))}{\sqrt{1+x^2y^2}}\ dxdy$$ ...
Max's user avatar
  • 155
2 votes
0 answers
75 views

How can I make sure that when I write in the wolfram language, I'm writing exactly what I intend (or what others are writing)? [closed]

I'm someone who is just starting to do some hobbyist math on my own, using various tools like wolfram alpha, and I have a question about the wolfram command line. My question is as follows I'm not ...
Wayferer Alpha's user avatar
1 vote
1 answer
63 views

Finding constant term in product expression

I've an expression which is product of 20 or more factors of polynomial, something like $$\left(1-\frac{pq}{z^i}\right)(1+pq z^j+z^k)$$ and I want to find coefficient of $z^0$. SeriesCoefficient works ...
xandar's user avatar
  • 13
0 votes
0 answers
41 views

Perturbing a tensorial expression

I am new to Mathematica. I am trying to simplify an expression of the some form like: $$ n_i \sigma_{ij} n_j - \gamma n_i \hat{\sigma_{ij}} n_j = 2 + v_i x_i + \kappa E_{ij} \chi_{ji} $$ There are ...
fiarast11's user avatar
3 votes
2 answers
224 views

Can Mathematica simplify an ordinary differential equation (ODE) by assuming a power series solution and obtain the recurrence relation?

I have an ordinary differential equation and want to solve it using power series as ψ[x_] = Sum[Subscript[a, n] x^n, {n, 0, ∞}] to obtain the recurrence relation ...
PhysFan's user avatar
  • 63
0 votes
1 answer
54 views

Truncation by coefficient size

I have a series with e.g. Chebyshevs: $\sum_i^N a_i T_i(x)$ where they are decreasing in size with increasing $i$. So now suppose I multiply two such series: $(\sum_i^N a_i T_i(x))(\sum_i^N b_i T_i(x))...
Confuse-ray30's user avatar
1 vote
0 answers
88 views

Strange behavior of error function series expansion at infinity

Evaluating Normal[Series[1/ (1 + xi Erf[xi]), {xi, ∞, 2}]] Normal[Series[1/( xi (1/xi + Erf[xi])), {xi, ∞, 2}]] gives ...
ssskkkky's user avatar
1 vote
0 answers
43 views

Identification of terms

I have the following sum on terms: ...
Ruth Murphy's user avatar
1 vote
1 answer
120 views

Limit of Hypergeometric Functions

Mathematica (12) seems to have a lot of trouble with taking limits involving hypergeometric functions. A simple example I am interested in is the following ...
Rudyard's user avatar
  • 471
2 votes
1 answer
148 views

Asymptotic solution of a system of ODEs

I have the following system of Ordinary Differential Equations (ODEs) together with initial values ...
yarchik's user avatar
  • 19.2k
1 vote
0 answers
58 views

Series behavior for self-defined function

How to make Series give the correct expansion of a self-defined function? For example, for some reason, I use f[x] to represent ...
Crack-Hu's user avatar
2 votes
1 answer
170 views

BUG: Why is Series[] getting this expression wrong?

EDIT: Wolfram confirmed this is a bug in Series[], and they're looking into it. I'm trying to generate a 2nd-order Taylor series in theta for a complicated expression "mdel" using Series[...
Jerry Guern's user avatar
  • 4,632
1 vote
1 answer
71 views

Expanding polynomials using valuation

I would like to expand the polynomial $p(\lambda) = \sum_{i=0}^{d} a_{i} \lambda^{i}$, as $F(p(\lambda), \lambda_{0})= \min_{j} [ val(a_{j}) + j \lambda_{0} ] $ with $\lambda_{0}$ being a real ...
Shasa's user avatar
  • 1,043
3 votes
3 answers
193 views

Evaluating series expansion is very slow

I need in my work to get series expansion of (2 E^x x HypergeometricPFQ[{1}, {1/2 + E^-x/4, 1 + E^-x/4}, -(x^2/4)])/Gamma[E^-x/2] + x^(1 - E^-x/2) Sin[x] up to $n=...
Mohamed Mostafa's user avatar
1 vote
0 answers
121 views

How can I fully simplify sum that includes absolute value?

Consider the following sum: ...
Rick Li's user avatar
  • 11
9 votes
2 answers
402 views

Why does Mathematica get the infinite sum of this representation of the taylor series of $\cos^2(x)$ wrong?

Bug introduced in 12.0 or earlier, persisting through 13.2 or later Mathematica correctly identifies this sum as $\cos(x)$: ...
Samuel Martineau's user avatar
2 votes
3 answers
158 views

Find Generalized Series with Symbolic Variable

CoefficientList[Series[Exp[x], {x, a, 3}], x] Gives the following expression, $$ \left\{-\frac{1}{6} e^a a^3+\frac{e^a a^2}{2}-e^a a+e^a,\frac{e^a a^2}{2}-e^a a+e^...
Torkoal's user avatar
  • 153
3 votes
2 answers
183 views

First argument -h is not a valid variable

I am trying to simpligy my life by defining a function that gets the series expansion of $f(x+h)$ and $f(x-h)$ (at $x=0$) by the following code, ...
kichapps's user avatar
1 vote
0 answers
63 views

Limit giving indeterminate result

I have a function $r_h(v)$ given by, $$r_h (v) = \left(\frac{m_0}{2 g} e^{-g v_f} \left(-1+e^{-g(v - v_f)} \right) \right)^{1/5}$$ where $m_0$ and $g$ are just numbers. I want to take the limits of ...
mathemania's user avatar
0 votes
0 answers
101 views

How to solve recurrence equation using RSolve?

How can I solve the following recurrence equation while I dont have the initial values? Is it possible to solve this using RSolve? ...
mehrosadat ebrahimi's user avatar
1 vote
0 answers
85 views

Series expansion message with special functions

I am trying to expand the following expression in alp,eps. Since the expression involves Hypergeometric2F1, I am using HypExp. <...
BabaYaga's user avatar
  • 1,897
1 vote
0 answers
25 views

Finding the coefficients of a decomposition of complicated expression into products of special functions

I have the following expression which arises while studying minimal models in CFT. The 4-point amplitude of scalars is given by $$G(z,\overline{z}) = ((1-z)(1-\overline{z}))^{\frac{m-1}{m+1}}\mathcal{...
QFTheorist's user avatar
2 votes
1 answer
78 views

An apparent error with Chebyshev polynomials

I am on 11.0.1.0 SeriesCoefficient[ChebyshevU[n,x],{x,0,m}] returns ...
მამუკა ჯიბლაძე's user avatar
1 vote
1 answer
91 views

Proving an expression from Mathematica which is clearly visible from Plots

I have the following Mathematica code: ...
codebpr's user avatar
  • 2,433
1 vote
0 answers
92 views

Trying to use Linear Optimization to solve inequalities

I am trying to use Mathematica to get bounds on some quantities using a certain procedure which is called conformal bootstrap. For the users who don't come with a background in HEP, I am basically ...
QFTheorist's user avatar
2 votes
1 answer
120 views

How to convert DifferenceRoot into a special function?

Clear["Global`*"]; f[z_] := z^(2 m) /(1+z)^m res = SeriesCoefficient[f[z], {z, -1, -1}, Assumptions -> Element[m, PositiveIntegers]] The result ...
lotus2019's user avatar
  • 2,151
1 vote
1 answer
120 views

Series expansion of Beta function in Mathematica

How one should do the series expansion of Beta function $B(x,y)=\frac{\Gamma(x)\Gamma(y)}{\Gamma(x+y)}$ around an arbitrary negative integer let's say $x=-k$ and $y=-l$? I want a symbolic expression ...
Hkw's user avatar
  • 39
1 vote
1 answer
133 views

A request on the kernel of the function ”SpheroidalEigenvalue“ in Mathemitica 11

I want to understand the algorithm of the function "SpheroidalEigenvlaue" in Mathematica 11, especially the code of the following command. Then I will try to use this algorithm to reproduce ...
amon xu's user avatar
  • 41
4 votes
1 answer
115 views

A simple series expansion which seems to be wrong

Trying to answer this question, I made the following input FullSimplify[SeriesCoefficient[ArcTanh[x]/(1 + x^2), {x, 0, n}]] I shall not type the results but, not ...
Claude Leibovici's user avatar
0 votes
1 answer
84 views

Series expansion for expression with parameter?

I would like to compute the following expansion. Series[(A + p/x^a)^2, {x, 0, 1}] where $a>0$. However Mathematica simply returns the expression, unless I ...
korni1990's user avatar
  • 307
0 votes
0 answers
176 views

How to solve or test the interval of Uniform Convergence of function series?

How to solve or test the interval of Uniform Convergence of function series? (ref2) e.g. $\sum_{k=1}^{\infty}\left(z^{k-1}-z^k\right)$ The convergence interval of this series can be got by ...
lotus2019's user avatar
  • 2,151
1 vote
1 answer
233 views

Discrepancy with Hurwitz Zeta function

I've come across an issue while using Wolfram Mathematica that I don't quite understand. Consider the following symbolic computation: ...
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