# Questions tagged [series-expansion]

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

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

Mathematica correctly identifies this sum as $\cos(x)$: Sum[((-1)^n x^(2 n))/(2 n)!, {n, 0, Infinity}] Mathematica also correctly identifies this product of sums ...
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### An apparent error with Chebyshev polynomials

I am on 11.0.1.0 SeriesCoefficient[ChebyshevU[n,x],{x,0,m}] returns ...
1 vote
82 views

### Proving an expression from Mathematica which is clearly visible from Plots

I have the following Mathematica code: ...
1 vote
85 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 ...
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### 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 ...
1 vote
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### 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 ...
1 vote
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### 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 ...
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### 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 ...
71 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 ...
115 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 ...
1 vote
215 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: ...
1 vote
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### 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 ...
185 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 ...
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### 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 ...
32 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 ...
1 vote
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### 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.
1 vote
66 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 ...
116 views

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

I started by defining ...
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### 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] ...
1 vote
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### 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 ...
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) y x]^2 around ...
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### 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 ...
119 views

### Can Mathematica estimate this complex function?

Mathematica has given me a function in $x,r$ given by ...
145 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? ...