Question:Calculating the outer product matrix

Question:Calculating the outer product matrix

Maple 2018

My question has two steps:

STEP 1:  The multiplication  of is defined as follows

if n<>l, then

.

if n=l and m<=s,

Question 1: I wrote a code for calculating the multiplication  of. Is it right?

The code for Step 1

```restart;

multiply:=proc(n,m,l,s) local g,a:
a:=unapply(doublefactorial(2*j-1)/factorial(j),j):
g:=unapply((a(m-j)*a(j)*a(s-j)/a(m+s-j))*(2*m+2*s-4*j+1)/(2*m+2*s-2*j+1),j):

if n<>l then 0 else
end if
end proc:

n:=2:
l:=2:
m:=1:
s:=1:
multiply(n,m,l,s);
```

when I compared the results which I got and the results which is given in the book as follows, I think it is right.

Step 2:

We know that the outer product matrix is calculated as follows

We found the elements of the outer product matrix in Step 1.

Question 2 : I want to write the elements which are derived in step 1 to the outer product matrix in step 2. In here, the outer product matrix is NxN matrix. N=(M+1).2^(K-1) where K, M are any integers.

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