HP 17B and HP 27S: Using the Solver for Recursive Functions
Introduction
A simple store and recall procedure can be used with the solver.
One Initial Condition
u_n = f(u_n-1) with the initial condition u_0
Let B = u_n and A = u_n-1, set up the solver as:
B = F(A)
Initial condition:
u_0 ( A ) ( B )
Subsequent calculations:
[ RCL ] ( B )* [ STO ] ( A ) ( B )
*RCL B is not necessary if you go straight to the next calculation.
Example:
u_n = 4*u_n-1 - 3, u_0 = 3
Setup: B=4×A-3
3 ( A ) ( B )
Result: 9
[ RCL ] ( B) [ STO ] ( A ) ( B )
Result: 33
[ RCL ] ( B) [ STO ] ( A ) ( B )
Result: 129
[ RCL ] ( B) [ STO ] ( A ) ( B )
Result: 513
Two Initial Conditions
u_n = f(u_n-1, u_n-2) with the initial conditions u_0 and u_1
Let C = u_n, B = u_n-1, and A = u_n-2 and set up the solver as:
C = F(A, B)
Initial condition:
u_0 ( A ) u_1 ( B ) ( C )
Subsequent calculations:
[ RCL ] ( B )* [ STO ] ( A ) ( B )
Example:
The Fibonacci Sequence:
u_n = u_n-1 + u_n-2; with u_0 = 1, u_1 = 1
Setup: C=B+A
1 ( A ) 1 ( B ) ( C )
Result: 2
[ RCL ] ( B ) [ RCL ] ( A ) ( C )
Result: 3
[ RCL ] ( B ) [ RCL ] ( A ) ( C )
Result: 5
[ RCL ] ( B ) [ RCL ] ( A ) ( C )
Result: 8
Nothing to it.
Eddie
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