Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!samsung!zaphod.mps.ohio-state.edu!pacific.mps.ohio-state.edu!tut.cis.ohio-state.edu!ucbvax!EN.ECN.PURDUE.EDU!wscott
From: wscott@EN.ECN.PURDUE.EDU (Wayne H Scott)
Newsgroups: comp.sys.handhelds
Subject: Bessel functions
Message-ID: <9002201947.AA24782@en.ecn.purdue.edu>
Date: 20 Feb 90 19:47:58 GMT
Sender: daemon@ucbvax.BERKELEY.EDU
Lines: 56


This is a function I wrote to aid in my study of FM signal modulation.
It computes the bessel function.
It expects n and x to be on the stack and it returns the result of the
bessel function.  
Note it is recursive so it should be named J or change the one reference
to this name within the program.

To anyone who enjoys HP28 optimization please work on this.  I know it can be
much faster but I just haven't had the time.

J
<< -> n x <<
   << IF n 0 < THEN
	 n NEG x J
	 n 2 MOD 2 * 1 - * NEG
      ELSE IF x 0 == THEN
	 n 0 ==
      ELSE
	 17.1032 .2639 n * + .6487 x ABS * + .0018 n * x ABS * -
	 .6457 n x ABS MAX * + 
	 .5 + FLOOR 2 / CEIL 2 *
	 0
	 1.e-50
	 DUP
	 DUP 2 *
	 0
	 0
	 -> m bkp1 tiny bk t bn bkp2 <<
	   m 1 - 0 FOR k
	      bkp1 'bkp2' STO
	      bk 'bkp1' STO
	      2 k 1 + * bkp1 * x / bkp2 - 'bk' STO
	      IF k n == bk THEN 
		 bk 'bn' STO 
	      END
	      IF k 0 > k 2 MOD 0 == AND THEN
		 t 2 bk * + 't' STO
	      END
	      if k 0 == THEN
		 t bk + 't' STO
	      END
	   -1 STEP
	   bn t /
         >>
      END
      END
   >>
>>

Ported from MatLab librarys

_______________________________________________________________________________
Wayne Scott             |  INTERNET:   wscott@en.ecn.purdue.edu
Electrical Engineering  |  BITNET:     wscott%ea.ecn.purdue.edu@purccvm
Purdue University       |  UUCP:      {purdue, pur-ee}!en.ecn.purdue.edu!wscott