Questions tagged [series-expansion]

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

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28 views

Force Mathematica to display `Series` in factorial notation

The Series expansion for Sin[Pi * x] is Series[Sin[Pi * x], {x, 0, 10}] Pi * x - (Pi^3 * x^...
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1answer
31 views

Optimizing a series expansion for high order in $x$

I would like to expand the following function at $x \sim 0$ up to some high $x_\text{max} = \Delta_\text{max}$: $$16 \sum_{\Delta=1}^{\Delta_\text{max}} \sum_{s=0}^{\Delta-2} f_{\Delta,s} \frac{(s+\...
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33 views

Series expansion of hypergeometric function with two variables

I have a function $g(x,y)$ that contains a product of hypergeometric functions, both involving the variables $x$ and $y$. I try to do a series expansion in the two variables as recommended in this ...
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63 views

Transforming a tensor expression

I have the expression $\qquad\sqrt{\det[\gamma^{\mu \nu} F_{\mu \nu}]}$ Basiclly, I need to expand this expression in some form like : $trF^4 + (trF^2)^2 + \sqrt{\det[F_{\mu \nu}]}$, where $\gamma^{\...
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40 views

Incorrect truncation of a series expansion

What is wrong here? fExp = f0 + f1 Sqrt[s] + f2 s + O[s]^(3/2); {s fExp + O[s]^(3/2),s f + O[s]^(3/2)/.f->fExp} Returns ...
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23 views

How to perform a series of an Integral with Respect to variable x which affects limits of integral

I am trying to approximate the effect of a parameter on an integral through a series expansion. The integrand depends on this parameter, but so do the limits of integration: $I(x)=\int_{t_1(x)}^{t_2(x)...
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1answer
48 views

Solving a system of differential equations (Use of Dsolve?)

I am hoping to solve the equations as follows, where 1H*, 3M* and 3E* are functions of t and all others are constants. I tried the code, ...
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3answers
97 views

Higher order Around, for large error propagation

TLDR question: How to redefine Around to work with higher order approximation. Motivation From the documentation Around ...
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2answers
123 views

Expanding logarithms in the negative domain

I am trying to expand some functions $f(z,\bar{z})$ containing logarithms for $z = x + i k x$ with $x<0$, but the results are not always consistent. As a simple example, consider the following code:...
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1answer
77 views

I failed to evaluate double integral

I try to evaluate this symbolic integral and evaluate its two series expansions according to certain variables, the plot the output providing some numerical values. This is a relativistic rotational ...
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26 views

Series Expansion Using Results from Reduce

I have a list of relations from using the Reduce function and I want to use them to get a series expansion in each variable. Here's what my relations look like: ...
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29 views

Iteratively Expanding Solutions in Multiple Variables

I've been working on a physics problem which requires finding the limiting behavior of variables as another variable goes to either zero or infinity. What I have is relations between 16 independent ...
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3answers
83 views

Make a series with coefficients taken from a list of values

I want to create a function $u(x) = \sum_{j=0}^9 a_j \cos{j\pi x}$ where the $a_j$s come from a list of random numbers. I tried the following ...
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38 views

AsymptoticSolve and Series not working in limit $\to \infty$. How to solve this functional polynomial relationship?

I want to solve for $J_d$ as a function of $n_d$ for $\eta\gg1$ and $\eta\gg\eta_0$ in the following equations by eliminating $\eta$ from the two equations. \begin{equation} J_d = J_0\cdot\left[\...
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1answer
31 views

Define a function of multiple arguments at a given point

Trivia I am using Taylor series expansions to solve a system of PDEs for a number of functions $f_1(z, \phi), f_2(z, \phi) ...$ The expansions are generated by ...
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1answer
64 views

How to get the convergence radius of the result of Series? [duplicate]

The Taylor expansion of function is very useful, but the convergence radius of power series results after Taylor expansion is also important. But the result of ...
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1answer
316 views

How to get the Taylor series of implicit functions

Given that the equation $x+\frac{1}{2} y^{2} +\frac{1}{2} z+\sin (z)=0$ can determine an implicit function $z(x,y)$ at {0, 0}, I now need to expand the implicit function $z(x,y)$ to a fourth-order ...
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1answer
60 views

Problem with Taylor expansion of a function

I need to make a Taylor expansion of the following expression: ...
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1answer
35 views

How to find expansion coefficients in Fourier-Legendre

I am trying to find the coefficients for the Fourier-Legendre expansion of a potential. My goal was to obtain the coefficients as expressions in terms of x and y. I followed the example given on the ...
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24 views

Help with a custom coordinate transformation

I'm just starting to use Mathematica and can't wrap my head around the task I have at hand. It comes from field-theory. (Sorry I had to insert formulas as images instead of proper LaTex as it would ...
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2answers
62 views

Why can't MMA find the series of this function at 0?

I want to expand the following two functions into series at x = 0, but MMA(Version 12.1.1) runs all the time and cannot return results: ...
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0answers
54 views

Why is this causing a Memory Allocation Failure? [closed]

This code causes an error. Why? It works fine if I cut the polynomial ff off at 12 terms instead of 15, but I can't understand why that would make a difference. Is the Series[] function just ...
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39 views

series expansion unpredictably dividing by leading coefficient

When expanding the simple expression expr = y^3 as a series in x, with expand = y -> Sum[Subscript[y, j] x^j, {j, 1, 20}]; ...
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2answers
106 views

Possible error with Series expansion

I'm expanding the following expression around x=1 ...
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1answer
71 views

Sum of Fourier Sine Series Not Giving Original Function

When I plug the below sum (from here) into Mathematica 12.1.1, why do I get something different from the original function ($1 + x^2$)? ...
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2answers
63 views

Use method “ExactAlgebraics” of PossibleZeroQ for Series zero test

I am trying to compute a series expansion around infinity with very large numerical, but entirely algebraic coefficients, and I keep running into zero test errors, which look exactly like the ones ...
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1answer
32 views

How can I find the maclaurin coefficients of different iterations of the same function?

I'm rather new to Mathematica so I would greatly appreciate any help. I want to find the series expansion coefficients of iterations of a function and export them as a .csv. Here is what I have ...
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58 views

Maclaurin series acting unusually

Here's my Mathematica code: ...
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1answer
29 views

Return exact solution in one variable from Series as an option

I have a module which expands many functions, depending on expansion order input parameters. Here's an MRE: ...
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31 views

How to calculate Laurent series in mathematica about some point zo and annulus a<|z|<b? [duplicate]

Can sameone tell me how to calculate Laurent series in mathematica about some point and annulus?
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2answers
394 views

Legendre expansion of the Dirac delta function

There is a known expansion for the Dirac delta function in the interval $ (-1, 1) $ in terms of the Legendre polynomials as $$ \delta(x) = \sum_{k = 0}^{\infty} (-1)^k \frac{(4k + 1) (2k)!}{2^{2k + 1} ...
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1answer
52 views

Series function not expanding an expression

I have the following code: FDE[d_, η_] := η^(d + 1)/Gamma[d + 2] + π^2/(6*Gamma[d])*η^(d - 1); Series[FDE[d/t, 1/η]/FDE[d/t - 1, 1/η], {η, 0, 3}] The series ...
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46 views

Why doesn't Mathematica provide an answer while Wolfram|Alpha does, concerning a series convergence?

Among other series I've been working on, I was asked to find whether $$\sum_n 1-\cos(\frac{\pi}{n})$$ converged, and Mathematica's output to ...
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36 views

How do I neglect suppressed terms in an expression?

I have an expression along the lines of expression = a^2 + a + b^2 + a*b Each variable has a big-O notation scaling, e.g. a ~ ...
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42 views

Approximation of roots using Series

I am solving a fifth degree polynomial using Series. My equation looks like ...
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1answer
44 views

Applying the command “expr/.rule”, to find the expansion of Cos[a+b]

how can i find the expansion of Cos[a+b], using the expression g[f[{a,b}]].So i am specified to use one shot replacement to get the expansion by replacing the argument of the expression given. I tried ...
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1answer
40 views

Division by a series with no coefficients

I know it is strange, but it seems MA is unable to compute a simple series expansion ...
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55 views

Evaluate parameters before function uses them

I want to construct a power series: LP[s_] := With[{x = 1, R = 10, n = 1}, Sum[cc[i + n, n, x, R] s^i, {i, 0, 20}]] but it kinda takes a long time to compute the ...
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1answer
68 views

Pade approximation of vector or operator functions

PadeApproximant is a very useful function of MA that starts with a truncated Taylor series $$f(x)\approx\sum_{k=0}^{l} c_k (x-x_0)^k,$$ and represents them in a ...
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29 views

Solving a system of numerical equations from a truncated series

I have an equation of the following sort: $$\sum_{s=0}^\infty c(s)f(s,x) = g(x), \tag{1}$$ where everything is real and $s$ is an integer. I know $f(s,x)$ and $g(x)$ numerically for any $s$ and any $...
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31 views

Truncate series with real powers that are not fully numerical

Take a function with the following expansion A3[z_]:=Sum[Subscript[a3x, jj]*z^jj, {jj, 0, 2}] + z^r Sum[Subscript[a3NAx, jj]*z^jj, {jj, 0, 1}]; where ...
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1answer
89 views

How do you find the Inverse of Elliptic Integral of Second Kind when modulus is large

So I tried to take the inverse of EllipticE when modulus is large, in Mathematica, but the solution gives wrong answer. ...
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1answer
66 views

Mathematica integrates centered functions, but can not integrate shifted ones

Mathematica seems to integrate this function: $\int \limits_{-\infty}^{\infty} d w\, \frac{\sin ^2\left(\frac{1}{2} wt \right)}{w^2} \frac{\frac{\gamma ^2}{4}}{ \left(w^2+\frac{\gamma ^2}{4}\right)}$, ...
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1answer
94 views

AsymptoticDSolveValue multiple solutions

I'm trying to solve the following ODE asymptotically. $$y(x)^2 y'(x)^2-\left(\sqrt{2} x\right)^2 y'(x)^2+y(x)^2=0$$ From ...
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1answer
58 views

Expanding Determinant as Multilinear Alternating Function

I am working with the expression $$\det\big{|}f(-kx), f(-(k-1)x),\cdots,f(0),\cdots, f((k-1)x), f(kx), g(x)\big{|},$$ where $f,g\colon\mathbb{R}\mapsto \mathbb{R}^{2k+2}$, and want to use the Taylor ...
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2answers
51 views

How to do series expansion for functions which have symbolic parameters?

I would like to find the series expansion of (E^(x^k/k!) Gamma[k, x])/Gamma[k] for $k$ being a positive integer, up to the order of $x^{2k+1}$. Mathematica ...
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0answers
22 views

Multivariate Lagrange inversion

I know that the function InverseSeries (Reference here) provides an interface for the Lagrange inversion formula. However I can't find anything on the ...
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40 views

Bad Integral evaluation for Piecewise function

I have been trying to evaluate this symbolic function: f[ρ_, R_, α_, yp0_, yp_] := R*((ρ - R*Cos[α])^2 + (R*Sin[α])^2 + (yp-yp0)^2)^(-(1/2)); Mathematica can ...
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2answers
65 views

Series can not expand the following root object about infinity. Is there another way to expand it?

I have the following equation which I want to solve it for r: ...
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34 views

Need help with Limit (DirectedInfinity)

I tried to compute the following limit: ...

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