A Padé approximation is the use of a ratio of polynomials to approximate a function. This can be seen as a generalization of the Taylor series which can better account for singularities in the function.

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### How to calculate two-point Padé approximant?

Wikipedia mentions two-point Padé approximant. I don't have access to the reference provided (Yoshiki Ueoka, Introduction to multipoints summation...). I checked also chapter 8 (The N-Point Padé ...
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I am trying to model the Pade approximation of a Lorentzian graph from the taylor series. I am trying to model PA[2/2] from taylor series expansion of order N+M=4th order of derivatives taken at the ...
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### Inequality of exponential function compared to its rational (Padé) approximation

In the context of studying the convexity of the real function (which is not DCP-convex but really "looks" convex) $$g(x) = \frac{1}{1-\exp(-1/x)}, \text{for } x\geq 0,$$ after some ...
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### How would I generate a Pade Approximant using the coefficients of a Taylor Series?

I would like to find an effective way to make a Pade Approximant using the coefficients of a Taylor Series. I've heard of Wynn's epsilon algorithm and using the Extended Euclidean Algorithm, but what ...
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Following wikipedia, I'm trying to compute the $[1/1]$-Padé approximation of $f(x)=x^2$. It should be of the form $\frac{a+bx}{1+cx}$, but this is either zero or a power series with a non-zero ...
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### Can a homographic function be approximated by an exponential function?

Can the homographic function: $$f(x)=\frac{1+\frac{x}{a}}{1-\frac{x}{1-a}}$$ where a ∈ (0,1), be approximated by an exponential function for the interval x ∈ [0,1-a] (where the function f(x) behaves ...
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### Padé approximant for non-linear least squares?

The Wikipedia article on Padé approximant makes it sound like "Padé series" is capable of approximating a function better than Taylor series can. Can Padé series be treated as a drop-in ...
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### Pade approximation for a function of 2 matrices

Is there any successful examples of using Pade approximation to calculate a function of 2 matrices, such as computing $C(A, B)$ such that $e^C = e^A e^B$? I know that Pade approximation has been ...
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### Pade approximation of a rational function

I believe I have a naive or hard question because I couldn't find any results in the Internet yet. Any help is greatly appreciated. So suppose I have two rational functions $R_1(x)$ and $R_2(x)$, i....
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### Why is the Padé approximant typically written in this form?

$$R(x) = \frac{\sum_{j = 0}^m a_{j} x^j}{1+\sum_{k=1}^n b_k x^k}$$ I've started computing these to approximate my coefficients for a regression and others have been asking me how the Padé approximant ...
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I would like to know how to code Pade Approximation on Mathematica. And also I have solved Eigen values and have 20 coefficient values,but I am not sure how to code on mathematica.Can you please ...
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### Show that $\exp(x)-\frac{1+\frac{x}{2}}{1-\frac{x}{2}} = O(x^3)$

I'm trying to show the following statement: $\exp(x)-\frac{1+\frac{x}{2}}{1-\frac{x}{2}} = O(x^3)$ I know that this is an example of Padé Approximation of the exponential. But I am not allowed to ...
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### How can I get those approximations?

Suppose, $u$ is the unique real solution of $x^x=\pi$ and $v$ is the unique real solution of $x\cdot e^x=\pi$ Expressed with the Lambert-w-function we have $u=e^{W(\ln(\pi))}$ and $v=W(\pi)$ Wolfram ...
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