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How to find the Direct Discrete Laplace Transform of ${2n \choose n}$

Some time ago I developed a discrete version of the Laplace transform for the purpose of calculating sums and solve finite difference equations with constant coefficients. The notes below are a ...
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discretize a function using $z$-transform

I would like to discretize the following continuous function using $z$-transform: $$G(s)=\frac{s+1}{s^2+s+1}$$ The process I am using is to take the inverse Laplace transform of $\frac{G(s)}{s}$ and ...
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How do I apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$?

I want to apply partial fraction expansion on $\dfrac{K}{(a+bz^{-1})(x+yz)}$. I'm not able to do it in the standard way, because one term has $z^{-1}$ term and the other has $z$. What is the approach ...
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I'm trying to solve the following recurrence using Z transforms: For $n\in \mathbb{N}^{*}$ $T(n)=1\ for\ n< 4$ $T(n)=T(\lfloor \frac{n}{4} \rfloor)+T(\lfloor \frac{3n}{4} \rfloor)+n\ for\ n\geq ... 0answers 6k views Relationship Between The Z-Transform And The Laplace Transform Below I've quoted Wikipedia's entry that relates the Z-Transform to the Laplace Transform. The part I don't understand is$z \ \stackrel{\mathrm{def}}{=}\ e^{s T}$; I thought$z\$ was actually an ...
Yesterday ago I was reading how the Laplace Transform can be interpreted as the continuous analog of the discrete functional dependance of the power series $$f(x) = \sum a(n) x^n$$ This is to say, ...