color graphic of a function in matlab

hi i need to write this in matlab and make a graphic that looks like this

i need to put the function in a code and make this graphic i dont know how to do either

Answer 1

[Walter Roberson]

Example:

xvec = linspace(0,10*pi, 100);
yvec = linspace(0,5*pi, 50);
[Xg, Yg] = meshgrid(xvec, yvec);
Zg = sin(Xg) .* tanh(Yg);
h = pcolor(Xg, Yg, Zg); set(h, 'edgecolor', 'none')

You will need to figure out how to effectively do the infinite summation.

[Samuel Molinari]

thx you so much for helping me!

[Walter Roberson]

Unfortunately I do not seem to find any nice ways to restate the infinite sum.

[Walter Roberson]

What kind of values are there for a and b ? Some of the values I tested with lead to divergent sums.

[Samuel Molinari]

a=infinit and b=pi

[Samuel Molinari]

where do i write them?

[Walter Roberson]

if a is infinity and b is pi then the denominator is n*sinh(n*a*pi/pi) which is n*sinh(n*infinity). For all positive n that is n*sinh(infinity) and positive times infinity is positive infinity. So each term of the denominator is positive infinity.

When the denominator is infinity the results of the division are 0 except possibly if the numerator is infinity. Can the numerator be infinity? If y is positive then as n approaches infinity the sinh approaches infinity. But if x is positive then x*n approaches infinity and sin(infinity) is undefined, being anywhere in the range -1 to +1. You would need careful consideration of the possibility of +/-infinity divided by infinity. I suspect that the reasoning might be that the constant infinity in the denominator "approaches" infinity faster than the numerator that is not constant infinity, so I suspect that you always get 0, but I am not certain.

So for a infinity and b positive I believe that the sum is either 0 or (because of n infinite) undefined.

[Walter Roberson]

Maple says that with the denominiator being infinite that the terms are all 0 including at n = infinity.