Questions tagged [series-expansion]

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

Filter by
Sorted by
Tagged with
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
203 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
51 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
81 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
41 views

Identification of terms

I have the following sum on terms: ...
Ruth Murphy's user avatar
2 votes
0 answers
69 views

Series expansion of an action to get quadratic order terms of the perturbation

I'm trying to solve this paper (Eqs 6-11). The action is defined as $S = \frac{1}{2 \pi \alpha'}\int_{\Sigma} d\tau d\sigma(\sqrt{-\det g_{ab}}+ B_{mn} \partial X^m \partial X^n)$. where, $\tau=t$, $\...
Entangled Quark's user avatar
1 vote
1 answer
93 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
  • 461
2 votes
1 answer
132 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
  • 18k
0 votes
0 answers
57 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
166 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
  • 4,602
1 vote
1 answer
67 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
  • 961
3 votes
3 answers
181 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
117 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
391 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
153 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
171 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
0 votes
0 answers
52 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
98 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
80 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
  • 1,746
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
75 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
87 views

Proving an expression from Mathematica which is clearly visible from Plots

I have the following Mathematica code: ...
codebpr's user avatar
  • 1,921
1 vote
0 answers
90 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
108 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
  • 2,091
1 vote
1 answer
106 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
129 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
  • 31
4 votes
1 answer
112 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
83 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
139 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
  • 2,091
1 vote
1 answer
221 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: ...
stefan_chem's user avatar
1 vote
1 answer
50 views

How to obtain a list of pairs of exponents in a double series expansion?

Let's say we have a function of two variables $f(x,y)$ and we work out its Taylor expansion up to some power. I would like to use Mathematica to construct a list of all exponents that appear in the ...
user1620696's user avatar
2 votes
0 answers
189 views

How to approximate an exponential series?

Consider the following expression $$ y_j= \sum_{k=0}^{L} \frac{e^{-\sum_{i=-k}^k(k-|i|)x_{j+i}}-e^{-\sum_{i=-k}^k(k+1-|i|)x_{j+i}}}{\sum_{i=-k}^k x_{j+i}}\tag{1} $$ for $1\leq j \leq L$. Given smooth ...
sam wolfe's user avatar
  • 4,553
1 vote
1 answer
88 views

Comparing two power series and extracting their coefficients

I have a standard mathematical problem that I was wondering how to solve efficiently by mathematica. Here is the problem. I have two power series expansions of a function ...
Physics Moron's user avatar
0 votes
0 answers
34 views

Weird expression for function Series-Expansion with Gamma function for different values of gamma coefficient

I extract the function jin[r] by solving eqsynin, and then I develop the function's series (around zero) to generate an equation for m1in and m2in based on esyn and gamma, knowing that the function ...
Pantelis Ashikkis's user avatar
1 vote
1 answer
125 views

How to expand $\frac{1}{(1-z-z^2)}$ into a power series [closed]

How can I get Mathematica to expand $$\frac{1}{(1-z-z^2)}$$ into a power series so that I can pick out the coefficients.
Vectorizer's user avatar
1 vote
0 answers
70 views

How to accelerate Inverse[] for positive definite matrices symbolically?

I am trying to construct a positive definite matrix based on the multiquadric radial basis function (RBF) for a set of thirteen points symbolically in order to later approximate the Laplacian operator ...
Faz's user avatar
  • 1,817
4 votes
1 answer
117 views

Why `AsymptoticSolve` doesn't work for a multivariate implicit function?

I started by defining ...
Nekomiya Kasane's user avatar
0 votes
0 answers
34 views

Attempt to evaluate a series returning Indeterminate while running Plot

I have a function in the form of a Series from a prior calculation: sol2D = SeriesData[a, 0, {Rational[3, 16] Pi, Rational[-5, 2], Rational[3, 4] Pi}, 0, 3, 2] ...
CuriousOkapi's user avatar
1 vote
0 answers
115 views

Taylor series loop

I'm a beginner not only in Mathematica but also in programming in general, and so I'm not really sure where my problem lies exactly and I'd be glad to receive any guidance. Using the Taylor series for ...
milf_and_cookies's user avatar
2 votes
1 answer
81 views

Why does Series give two different results for given function?

I want to do Series of this function x^12 Cos[y x]^2 Sin[y x]^6 Sin[(-1 + Sqrt[3]) y x]^2 around ...
Martha97's user avatar
  • 349
2 votes
1 answer
110 views

Making Series Solutions Look Nicer

My students and I are using AsympototicDSolveValue[] to find power series solutions to linear differential equations at 0. For example, the following code gives me a solution up to degree 7. I'm ...
B flat's user avatar
  • 5,513
0 votes
1 answer
119 views

Can Mathematica estimate this complex function?

Mathematica has given me a function in $x,r$ given by ...
Matthew Neil's user avatar
2 votes
1 answer
176 views

How to obtain the Taylor expansion of any function? [duplicate]

How to obtain the Taylor expansion of any function? Like the Taylor expansion of any function in the picture. How can I obtain the Taylor expansion of any function if I input it? ...
csn899's user avatar
  • 3,635
0 votes
0 answers
23 views

Different results for same output

In a power series solution method, I am trying to find the roots of an equation. By changing the parameters I need to get the roots. The problem is the parameter value is provided as 0.15 which gives ...
supragyan priyadarshinee's user avatar
4 votes
4 answers
222 views

Solving PDE with power series

I would like to solve the PDE $$\partial_{x}f(x,y) + f(x,y)^2 = g(x,y)$$ with $f(0,0)=0$ and $\partial_y f(0,0)=0$ using a power series ansatz, i.e. I have an explicit expression for $g(x,y)=\sin(x+y)\...
António Borges Santos's user avatar
0 votes
0 answers
69 views

Approximating Exp[-x] in partial fraction form [duplicate]

I'm looking to obtain order-$k$ approximation of $\exp(-z)$ for real-valued $z$. $$R_k(z)\approx \exp(-z)$$ The constraint is that I need the result in partial fraction form, ie: $$ \begin{equation} ...
Yaroslav Bulatov's user avatar
3 votes
1 answer
67 views

Approximating exponential generating function (EGF) from values of generating function (OGF)

I have a function that can evaluate ordinary generating function, and need to construct an approximation to the exponential generating function by using a few calls to the ordinary generating function....
Yaroslav Bulatov's user avatar
4 votes
1 answer
343 views

Zassenhaus formula in Mathematica

I'm looking for Mathematica implementation of Zassenhaus formula -- given two matrices $A,B$, truncate the expansion of $\exp(A+B)$ from this paper: $$e^{t(A+B)}= e^{tA}e^{tB}\prod_{n=2}^\infty e^{t^n ...
Yaroslav Bulatov's user avatar
2 votes
2 answers
232 views

Series expansion using binomial theorem in Mathematica

The series expansion of $\displaystyle\left(1-\frac{a}{x}\right)^{1/3}$ using the Binomial theorem is given by $$\displaystyle\left(1-\frac{a}{x}\right)^{1/3}=1-\frac{a}{3x}-\frac{a^{2}}{9x^{2}}-\...
VH84's user avatar
  • 179
0 votes
1 answer
47 views

Solving series solution of differential equation

AsymptoticDSolveValue[2x*y''[x] -(3+2x)*y[x] +1 == 0, y[x], {x, 0, 5}], this differential equation command, is not outputting the correct solution. The solution should be like y=C1(1+(1/3)x-(1/6)x^2-(...
haha97894's user avatar

1
2 3 4 5
18