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How to Plot a function that contains summation?

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How can I plot the attached two functions with limits from -pi to pi for different values of m ?
  5 Comments
Walter Roberson
Walter Roberson on 20 Sep 2021
x=[-pi:0.1:pi]
x = 1×63
-3.1416 -3.0416 -2.9416 -2.8416 -2.7416 -2.6416 -2.5416 -2.4416 -2.3416 -2.2416 -2.1416 -2.0416 -1.9416 -1.8416 -1.7416 -1.6416 -1.5416 -1.4416 -1.3416 -1.2416 -1.1416 -1.0416 -0.9416 -0.8416 -0.7416 -0.6416 -0.5416 -0.4416 -0.3416 -0.2416
figure
for alpha=1:10
m = (1:alpha).';
Function_5 = (pi/2) + sum(((2 .* (-1).^m-1) .* cos(m.*x) ./ (pi .* m.^2)),1);
plot(x, Function_5, 'displayname', "\alpha = " + alpha);
hold on
end
legend show

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Accepted Answer

Walter Roberson
Walter Roberson on 20 Sep 2021
alpha = 8;
m = (1:alpha).';
f = @(x) 2/pi + sum(2 .* ((-1).^m - 1)./(pi .* m.^2) .* cos( m.*x ), 1);
fplot(f, [-pi pi])
  3 Comments
Walter Roberson
Walter Roberson on 20 Sep 2021
syms x m
figure
for alpha=1:10
Function_5 = (pi/2) + symsum(((2*(-1)^m-1)*cos(m.*x)/pi*m^2),m,0,alpha);
fplot(Function_5, [-pi pi], 'DisplayName', "\alpha = " + alpha);
hold on
end
legend show

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