Hi all:

In a different thread (Gerson W. Barbosa's "alternative cos(x) and tan(x) [HP-33S]"), Les Wright posted:

*"[...] Unfortunately the routines don't keep the entire stack in its original state, but this is a nice touch. One problem about RPN programs is they make a mess of the stack sometimes, unlike the internal routines."*

- The HP35S' ability to mix RPN and algebraic equations in a single program in RPN mode can be used to perform what you want, i.e., program a complicated function that behaves as built-in ones, i.e., the argument is taken from ST X, ST X is replaced by the function's value, and the original argument is stored in LAST X.

For instance, suppose that you want to program a two-term version of Stirling's approximation to the factorial function X!, namely:

f(X) = (X/e)^X*Sqrt(2*Pi*X)*(1+1/(12*X)+1/(288*X^2))and you want it to behave as a built-in function as far as stack behaviour is concerned. You can achieve that in the HP35S without using any auxiliary registers or variables with this simple trick, key in this little proof-of-concept program in your HP35S:

A001 LBL A

ABS

Roll Down

(LASTx/e)^LASTx*SQRT(2*Pi*LASTx)*(1+INV(12*LASTx)+INV(288*LASTx^2))

A005 RTN

where I've used "/" to denote the division key and "*" to denote the multiplication key, as well as "Pi" to denote the Pi key.

To run it, just key in you argument in ST X, and XEQ A [ENTER]: the result will be returned to ST X, the previous contents of ST X will be stored in LASTx, and the rest of the stack will be unaffected.

For instance, in FIX 4, press:

4 [ENTER] 3 [ENTER] 2 [ENTER]Perhaps this is a little slower than pure RPN, but quite convenient indeed. Of course the same trick will work with any f(X) you care to define as long as it can be defined as an equation.

5 [XEQ] A [ENTER] -> 120.0025

[ROLLDOWN] -> 2.0000

[ROLLDOWN] -> 3.0000

[ROLLDOWN] -> 4.0000

[LASTx] -> 5.0000

I'll hope you'll like this little neat technique but if not, just stick to pure RPN and you'll be no worse than before :-)

Best regards from V.