[Maxima-commits] CVS: maxima/archive/share/trash airy.usg,NONE,1.1

[Robert D. <rob...@us...>]

Update of /cvsroot/maxima/maxima/archive/share/trash
In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv24472/archive/share/trash

Added Files:
	airy.usg 
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Move share/specfunctions/airy.usg to archive/share/trash/airy.usg.
(Useful content of airy.usg has been merged into doc/info/Special.texi.)


--- NEW FILE: airy.usg ---
		May 2, 1981 4:52 pm by Leo P. Harten (LPH)

The Airy equation diff(y(x),x,2)-x*y(x)=0 has two linearly independent
solutions, taken to be Ai(x) and Bi(x). This equation is very popular
as an approximation to more complicated problems in many mathematical
physics settings.

Do LOAD("AIRY");  to get the functions AI(x), BI(x), DAI(x), DBI(x) .

The file SHARE1;AIRY FASL (by LPH@MIT-MC) contains routines to compute the 
Ai(x), Bi(x), d(Ai(x))/dx, and d(Bi(x))/dx functions. The result will be
a floating point number if the argument is a number, and will return a
simplified form otherwise. An error will occur if the argument is large
enough to cause an overflow in the exponentials, or a loss of 
accuracy in sin or cos. This makes the range of validity
about -2800 to 1.e38 for AI and DAI, and -2800 to 25 for BI and DBI.
The GRADEF rules are now known to MACSYMA: diff(AI(x),x)=DAI(x),
diff(DAI(x),x)=x*AI(x), diff(BI(x),x)=DBI(x), diff(DBI(x),x)=x*BI(x).

The method is to use the convergent Taylor series for abs(x)<3.,
and to use the asymptotic expansions for x<-3. or x>3. as needed.
This results in only very minor numerical discrepancies at x=3. or x=-3.
More accuracy can be had if you request from LPH. For details,
please see Abramowitz and Stegun's
Handbook of Mathematical Functions, section 10.4 (hardcover ed.) and Table 10.11 .

To get the floating point Taylor expansions of the functions here, do 
ev(TAYLOR(AI(x),x,0,9),infeval); for example.

Please also try SHARE;BESSEL FASL (by CFFK) for the AIRY function there.


			Leo P. Harten (LPH)