DanA>I've never studied infinite matrix products, but would have expected that for one to converge, its general term would need to approach the identity. That's the less common case. It happened with those Sierpinski gasket Fourier series of a few yrs ago. DanA>No? (Or perhaps some entries "diverge to 0" ?) --Dan Yes. You can see that happened in the UL 2x2 of the RHS, below. The determinant approaches -63/256 and determines the convergence rate. Easier example: 1/n 1 0 e Prod ( ) = ( ) . n>0 0 1 0 1 --rwg I've found a 2F1[9/16] limiting case of the "Stone" that gives 12/pi and is tantalizingly close to Sun's matrix, below. Bashing it to coincide would prove the conjecture. << . . . prod(matrix([-(k+1/2)^3/(8*(k+1)^3),-(k+1/2)^2/(16*(k+1)^2),30*(k+7/30)],[-63*k*(k+1/2)^2/(16*(k+1)^3),0,0],[0,0,1]),k,0,inf) = matrix([0,0,24/%pi],[0,0,0],[0,0,1]) [ 1 3 1 2 ] [ (k + -) (k + -) ] [ 2 2 7 ] [ - ---------- - ----------- 30 (k + --) ] inf [ 3 2 30 ] [ 24 ] /===\ [ 8 (k + 1) 16 (k + 1) ] [ 0 0 --- ] | | [ ] [ %pi ] | | [ 1 2 ] = [ ] | | [ 63 k (k + -) ] [ 0 0 0 ] k = 0 [ 2 ] [ ] [ - ------------- 0 0 ] [ 0 0 1 ] [ 3 ] [ 16 (k + 1) ] [ ] [ 0 0 1 ] . . .>>