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Example: Convert the following algebraic expression to a series of objects in RPN syntax:

'A*COS(B+ƒ(C/D))-X^3'.

OA *TB +R!Ü

C/D ™™-XQ3 `%²RPN%

Bessel Functions

This section contains a program, BER, that calculates the real part Bern(x) of the Bessel function Jn (xe3πi/4). When n = 0,

( ) (x ⁄ 2)4 (x ⁄ 2)8 … Ber x = 1 – ---------------- + ---------------- –

2!2 4!2

Level 1

→

Level 1

 

 

 

z

→

Ber(z)

 

 

 

Techniques used in BER

Local variable structure. At its outer level, BER consists solely of a local variable structure and so has two properties of a user-defined function: it can take numeric or symbolic arguments from the stack, or it can take arguments in algebraic syntax. However, because BER uses a DO…UNTIL…END loop, its defining procedure is a program. (Loop structures are not allowed in algebraic expressions.) Therefore, unlike user-defined functions, BER is not differentiable.

DO…UNTIL…END loop (indefinite loop with counter). BER calculates successive terms in the series using a counter variable. When the new term does not differ from the previous term to within the 12-digit precision of the calculator, the loop ends.

Nested local variable structures. The outer structure is consistent with the requirements of a user-defined function. The inner structure allows storing and recalling of key parameters.

RPL Programming Examples 2-29