Jump to key moments of Pade Approx of Transfer Function

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The Exponential Function Learns To Wear PolesThis scene uses the classical Padé rational approximation of the exponential function. Instead of drawing arbitrary roots and poles, we start withRₙ(ζ) = Pₙ(ζ) / Pₙ(−ζ),where Pₙ is the diagonal Padé numerator for eᶻ. The roots of Pₙ become the zeros of the rational function, and the roots of Pₙ(−ζ) become its poles.Then the complex plane is gently warped by ζ = λ(t)eⁱᶿ(t)(z + c₂(t)z² + c₃(t)z³ + s(t))The visible pellets are the actual preimages of the
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📌The Padé approximant is a method used in mathematics to approximate a function using a ratio of two polynomials. Unlike a Taylor series, which uses only a polynomial to represent a function, the Padé approximant often provides a better approximation, especially near singularities or for functions with complex behavior. It is particularly useful in engineering, physics, and numerical analysis because it can offer more accurate results with fewer terms. This technique helps simplify complex func
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