# Tagged Questions

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### Padé approximant of transfer function with gain and time delay.

$$H(\omega) = A e^{-j \omega \tau}$$ I'm trying to use Padé approximation to generate a numerator and denominator polynomial for the above transfer function but genuinely struggling with how to ...
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### Approximations to the Roots of a Function

I want to find approximations to the root of a function in two variables using the Newton-Raphson method. I can use the method on a function in a single variable but I'm lost as to how you can use it ...
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### Approximately minimising a transcendental function.

I currently have a closed form solution for the error probability of a certain type of wireless channel. By letting all $S_i$ terms denote constants, using $U(\cdot,\cdot,\cdot)$ to denote the ...
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### Is there a known algorithm for approximating all the real and imaginary zeros of any well behaved equation of a single variable?

Does there currently exist a general algorithm (or set of algorithms used together) that will approximate all the zeros of any well behaved non-differential equation of a single variable which has a ...
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### $n \approxeq k + 2^{2^k}(k+1)$. How can one get the value of $k(n)$ from this equation?

I am trying to find approximation for this sum. Asymptotic approximation of sum $\sum_{k=0}^{n}\frac{{n\choose k}}{2^{2^k}}$ Doing following way. Let $a_k(n) = \frac{n\choose k}{2^{2^k}}$. I tried to ...
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### Dependence on Parameters of the Solution of a Non-linear Equation

I have the following equation for the delay in a queue\begin{align} d(f)=\frac{c(1-f)^2}{2(1-a)}+\frac{\lambda b}{2f(f-a)}\end{align} where $0\le f\le 1;\quad c,a=\lambda\tau, \ b=\tau^2$ or ...
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### Approximate solution for the root of a non-linear function

I have been working with a system which involves computing the roots of functions that look like $$e^t (g\cos(\omega t) + b) = c$$ where $t$ is the independent variable ...
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### General bound on a polynomial's root with the largest norm

Is there a general bound on a polynomial's root with the largest norm? When Rouche's theorem is used, it still seems that the polynomial's root with the largest norm still needs to be found if we ...
### Approximating roots of the truncated Taylor series of $\exp$ by values of the Lambert W function
To everyone: don't bother writing up another answer, i'm giving this bounty Antonio's answer. It just doesn't let me yet (24 hours delay). If you map the nth roots of unity $z$ with the function ...
### Complex Zeros of $z^2e^z-z$
Can anyone give me a hint on showing (in a relatively elegant way, as I know the answer from WolframAlpha), that the complex valued function $z^2e^z-z$ has at most 2 roots with norm less than 2? ...