atan Taylor Polynomial using polyval function.
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Jim Oste
am 17 Feb. 2015
Beantwortet: Evelia Coss
am 18 Feb. 2021
I need to write a function that computes the Taylor polynomial P_n(x) for a general odd number n>=1 using the built-in Matlab function polyval. I have the following function so far for the Taylor polynomial:
[ y ] = ost_arctanTaylor(n, x)
%Computes the Taylor polynomial for f(x) = atan(x)
for i = 1:2:n
y = ((-1).^(i)).*((x.^(2.*i-1))./(2.*i-1));
end
end
I am confused on how to integrate the polyval function into this code. Any help?
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John D'Errico
am 17 Feb. 2015
You are trying to evaluate the polynomial itself in a loop, although the loop as you wrote it will not do what you think.
The requirement was for polyval to evaluate it, NOT you. So you need to build the coefficients of the polynomial, and pass them into polyval. Let it do the work.
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John D'Errico
am 18 Feb. 2015
Polyval does not care if you give it zero coefficients. Make the even term coefficients zero. It WILL use those zero coefficients, effectively multiplying by zero, but who cares? You will just create a vector of coefficients, with the HIGHEST order coefficient first. So, for example, the atan series looks like
x - x^3/3 + x^5/5 ...
then the polynomial as polyval would care about it would be:
P = [1/5 0 -1./3 0 1 0];
Don't forget that zero'th order (constant) term at the end. It is important.
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Evelia Coss
am 18 Feb. 2021
x = input('Number that you want to analyze');
i = input('Number of iterations:');
% Create an cumulative variable
y = 0;
for n = 0:i
arctang = ((-1).^n).*(x.^(2.*n+1)./(2.*n+1));
y = y + arctang;
end
disp('Arctangent value of x is:');
disp(y);
I used the integral of arctang, see the link: https://math.stackexchange.com/questions/29649/why-is-arctanx-x-x3-3x5-5-x7-7-dots
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