HP 48gII Graphing, 50g Graphing manual Bessel Functions, XQ3 `%²RPN%, Techniques used in BER

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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 userdefined 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 userdefined 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 12digit pr ecision of the calculator, the loop ends.

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

RPL Programming Examples 229