Advanced Search

Question: Any comment, idea or innovation to calculate this parametric integral?

Question:Any comment, idea or innovation to calculate this parametric integral?

mehdibgh 240 Maple 2016
integration
January 14 2023
0

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

Note M, II, JJ are arbitrary positive integers (0<M, II, JJ<11).

F must be a function of Pm at the final!

``

> 

restart
> 

M := 3:
> 

JJ := 5
> 

II := 5
> 

with(ArrayTools):
> 

W := RandomArray(II, JJ, M):
> 

V := ArrayTools:-RandomArray(II, JJ, M):
> 

w := add(add(add(W[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):
> 

v := add(add(add(V[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):
> 

L := add(add((LegendreP(i-1, x)*LegendreP(j-1, y))^2, i = 1 .. II), j = 1 .. JJ):
> 

H := 1+tanh(w-v)
> 

F := int(H*L, [y = -1 .. 1, x = -1 .. 1])

Warning,  computation interrupted

  
> 

``
> 

``

Download integralproblem.mw
Please Wait...