# Any comment, idea or innovation to calculate this parametric implicit integral?

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Mehdi on 14 Jan 2023
Commented: Walter Roberson on 15 Jan 2023
Any comment, idea or innovation to calculate this parametric implicit integral?
Note M, II, JJ are arbitrary positive integers (0<M, II, JJ<11).
F must be a function of Pm at the final!
clear
M = 3;
JJ = 5;
II = 5;
W = rand(II, JJ, M);
V = rand(II, JJ, M);
p = sym('p',[1 M]);
syms x y
w = sym('0');
v = sym('0');
L = sym('0');
for m=1:M
for i=1:II
for j=1:JJ
w =w+W(i, j, m)*legendreP(i-1, x)*legendreP(j-1, y)*p(m);
v =v+V(i, j, m)*legendreP(i-1, x)*legendreP(j-1, y)*p(m);
L = L+(legendreP(i-1, x)*legendreP(j-1, y))^2;
end
end
end
H = 1+tanh(w-v);
F = int(int(H*L,x,[-1 , 1]), y,[-1, 1])
F = Walter Roberson on 15 Jan 2023
I am not clear as to what you are requesting?
The integral does not appear to be implicit, just not closed form.
If you are asking for a way to find a closed form expression for it, then I doubt that is possible.
You can use techniques such as taylor series, but that gets messy quickly and is going to be pretty inaccurate.

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