## Sunday, December 5, 2021

### HP 17B and HP 27S: Using the Solver for Recursive Functions

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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