How to calculate a recursive formula with three parameters in a matrix exponentiation way? Here is a recursive formula to computer Zernike polynomials, which is refer to "Recursive formula to compute Zernike radial polynomials," Barmak Honarvar Shakibaei and Raveendran Paramesran, Opt. Lett. 38, 2487-2489 (2013).

The built-in function ZernikeR's time complexity is O(n). We can find n’th Fibonacci Number in O(Log n) time using Matrix Exponentiation. Would it be O(Log n) if we compute Zernike polynomials in a matrix exponentiation way? Can we get a list of Zernike polynomials with different ms when n and r are fixed?