# Questions tagged [series-expansion]

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

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### Symbolic perturbation expansion for quantum mechanics using Hellmann-Feynman derivaties

I am interested in some quantum mechanical perturbation expansion for energies. Actually I want to implement these terms $E_n^{(k)}$. As is stated below one can do that using CAS. I would be ...
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### Another example where using FullSimplify gives different result than Simplify

I believe this question is very similar to Result of Series[expression] is different when I simplify the expression, however, due to my lack of Mathematica experience, I am reluctant to call it a bug. ...
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### Eliminating higher order trigonometric terms

I am interested in eliminating higher-order trigonometric terms from a long symbolic expression. Specifically I want to reproduce this simplification that is done (in a tutorial I am working through)...
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### Using Series with Refine or Assuming to restrict the power

I have a system of differential equations which contain a singular point. To avoid the singular point, I am expanding the coefficients and solutions in a power series around that point. Due to the ...
143 views

### Power series representation of MeijerG function, $G_{m,n}^{p,q}(x)$ [closed]

I've been experimenting with Mathematica and I keep getting the following (where $G_{m,n}^{p,q}(x)$ is the MeijerG function): Is it possible to express those $f_{i}(x)$ as a power series in $x$? ...
186 views

### Multivariate series for approximating implicit system

I'm trying to approximate the solution of an implicit set of equations by means of a Taylor series. I have managed to do so for a solution expressed in terms of a single independent variable, by using ...
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### Harmonic number of $r$ with order $r$ [closed]

Mathematica recently offered me this expression as the result of an evaluation: HarmonicNumber[r, -r]. I initially thought this must be equivalent to ...
191 views

### Hessian matrix product in Taylor expansion of vector function

I am trying to get the 2nd order coefficient of the Taylor expansion at $\pmb{x}=\pmb{0}$ of ...
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### Taylor series and falling factorials [closed]

I'm new in Mathematica and I have following problem to solve: If $f$ is any function $f: R \to R$ which can be represented as a Taylor series in some close neighbourhood $S$ of $0$ , is it true that ...
123 views

### Finding symbolic series coefficients

Is there any way to get the symbolic form of a series? For simple series this seems possible e.g. SeriesCoefficent[Exp[x],{x,0,n}] tells me that the general ...
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### How to do this series expansion with Mathematica

Consider for large integers $n$ the expression $\sin \left(\pi \sqrt{4 n^2+n}\right)$. Since $\sqrt{4 n^2+n}=2 n \sqrt{1 + \frac{1}{4 n}}$ we can use the standard series for the square root and ...
156 views

### Calculating the n-th term of the series expansion of a special function [closed]

I am trying to calculate the $n^{\text{th}}$ term of the following polynomial: $$\, _2F_1\left(-n,n+3;\frac{3}{2};x\right)$$ To do this I calculate: ...
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### Taylor Series of numerical solution of FindRoot

I have found the inverse to the following equation by using FindRoot. I want to have a Taylor approximation (say starting from ...
I am trying to linearize a vector expression $$\frac{(\mathbf{u}+d\mathbf{u})\times(\mathbf{v}+d\mathbf{v})}{\vert(\mathbf{u}+d\mathbf{u})\times(\mathbf{v}+d\mathbf{v})\vert}$$ Here is my code ...