Plotting infinite series on interval

I have the following function for error approximation

function y = Approx(x,N); 
Approx=zeros(1,length(x));
for n=0:N
    Approx=Approx+(((-1)^n)*x^(2*n+1))/((factorial(n))*(2*n+1));
    
end
Approx=(2/sqrt(pi))*Approx

My question is how would I plot this on a given interval say -1,1 as well as plotting it again the built in erf in Matlab

Answer 1

[Deepak]

Hi @jacob Mitch,

We can plot the approximation of the error function against built-in "erf" function in MATLAB by defining a MATLAB function "Approx" that computes the approximation using a series expansion. In a script, we generate a set of "x" values over the interval [-1, 1] and use the "Approx" function to calculate the approximation for these values. We also compute the built-in "erf" function for the same "x" values. Finally, we plot both the approximation and the built-in "erf" on the same graph for comparison, using distinct line styles and colors to differentiate them, and include labels and a legend for clarity.

Below is the MATLAB code to achieve the same:

% Define the approximation function
function y = Approx(x, N)
    Approx = zeros(size(x)); % Preallocate the Approx array for efficiency
    for n = 0:N
        Approx = Approx + (((-1)^n) * x.^(2*n+1)) / ((factorial(n)) * (2*n+1));
    end
    y = (2/sqrt(pi)) * Approx;
end

% Main script to plot the functions
% Define the interval and number of terms
x = linspace(-1, 1, 1000); % 1000 points between -1 and 1
N = 10; % Number of terms in the approximation

% Calculate the approximation and the built-in erf
approximation = Approx(x, N);
builtin_erf = erf(x);

% Plot the results
figure;
plot(x, approximation, 'r-', 'LineWidth', 2); % Plot approximation in red
hold on;
plot(x, builtin_erf, 'b--', 'LineWidth', 2); % Plot built-in erf in blue dashed line
hold off;

% Add labels and legend
xlabel('x');
ylabel('Function Value');
title('Approximation vs. Built-in erf');
legend('Approximation', 'Built-in erf');
grid on;

Please find attached the documentation of functions used for reference:

zeros: www.mathworks.com/help/matlab/ref/zeros.html

plot: www.mathworks.com/help/matlab/ref/plot.html

I hope this helps in resolving the issue.