Bessel Functions - HP 48gII Advanced User's Reference Manual

Graphing calculator
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Program:
END f +
»
ELSE 1 LIST SWAP DROP
END
»
`O"RPN K
Checksum: # 1522d
Bytes:
181.0
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 ™™-X Q3 `%²RPN%

Bessel Functions

This section contains a program, BER, that calculates the real part Ber
When n = 0,
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.
x 2
---------------- -
Ber x
=
1
2!
Level 1
"
"
z
Comments:
Append the function to the end of
the list.
End the local variable defining
procedure.
For functions with no arguments,
converts to a simple list.
End the IF...THEN...
ELSE...END structure.
Stores the program in "RPN.
(x) of the Bessel function Jn (xe
n
4
8
x 2
---------------- - –
+
2
2
4!
Level 1
Ber(z)
RPL Programming Examples 2-29
3 i/4
).

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