MATLAB: Expanding a function in power series

expansionfunctionpowerseries

Hi, I would like to expand an exponential function in terms of a power series. How can this be done in MATLAB, where one gets an output with say, the first 20 terms of the series?

Thanks!

Best Answer

help taylor

Best wishes

Torsten.

Related Solutions

MATLAB: Expanding a given function as a power series

You need the symbolic toolbox for this problem!

syms x y
f(x) = x^3+2*x;
g = f(exp(y));
g_approx = taylor(g, y, 'Order', 10)

Result

>> g_approx
g_approx =
(3937*y^9)/72576 + (6563*y^8)/40320 + (2189*y^7)/5040 + (731*y^6)/720 + (49*y^5)/24 + (83*y^4)/24 + (29*y^3)/6 + (11*y^2)/2 + 5*y + 3

MATLAB: How Should Conditional Mean and Variance Model be Changed if Residuals Exhibit Autocorrelation

It depends on the autocorrelation. If the autocorrelation occurs at a certain lag, then add a MA term at that lag. If the autocorrelation is a several lags, add AR terms. Another method is that you add AR and MA lags until the autocorrelation disapears. Check the T-values of the coefficients and remove those terms with insignificant coefficients. It is a bit of a trial-and-error process. Add terms and see if you can remove the autocorrelation. However, keep an eye on the T-values. The same process applies for removing the heteroscedasticity.

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Related Solutions

MATLAB: Expanding a given function as a power series

MATLAB: How Should Conditional Mean and Variance Model be Changed if Residuals Exhibit Autocorrelation

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