{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve
tica-bold-r-normal--14-*" "helvetica" "Helvetica-Bold" 8 12 0 "He
lvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--14-*" "ti
mes" "Times-Roman" 4 12 64 "Times-Roman" 12}{FONT 2 "-*-Courier-m
edium-r-normal--*-120-*-*-m-*-*-*" "Courier" "Courier" 4 12 192 "
Courier" 12}{FONT 3 "-adobe-new century schoolbook-medium-r-norma
l--*-240-*-*-*-*-*-*" "new century schoolbook" "Times-Roman" 4 24
 64 "Times-Roman" 24}{FONT 4 "-adobe-new century schoolbook-mediu
m-r-normal--*-240-*-*-*-*-*-*" "new century schoolbook" "Times-Ro
man" 4 24 64 "Times-Roman" 24}{FONT 5 "-adobe-new century schoolb
ook-medium-r-normal--*-240-*-*-*-*-*-*" "new century schoolbook" 
"Times-Roman" 4 24 64 "Times-Roman" 24}{FONT 6 "-adobe-new centur
y schoolbook-medium-r-normal--*-240-*-*-*-*-*-*" "new century sch
oolbook" "Times-Roman" 4 24 64 "Times-Roman" 24}{FONT 7 "-adobe-n
ew century schoolbook-medium-r-normal--*-240-*-*-*-*-*-*" "new ce
ntury schoolbook" "Times-Roman" 4 24 64 "Times-Roman" 24}{SCP_R 1
 0 70{COM_R 2 0{TEXT 1 225 "Maple Worksheet for Hankel Functions:
 Sample Usage\015\015Author: Douglas B. Meade\015                \+
Department of Mathematics, University of South Carolina, Columbia
, SC 29208\015E-mail: meade@math.scarolina.edu\015\015Created: 21
 July 1993\015"}}{SEP_R 3 0}{COM_R 4 0{TEXT 1 69 "Call in definit
ions and define common aliases (to simplify commands)\015"}}
{INP_R 5 0 "> "{TEXT 0 70 "with(share): readshare(hankel, program
); # load from the share library"}}{OUT_R 6 0 5{TEXT 2 71 "See ?s
hare and ?share,contents for information about the share library\
012"}}{OUT_R 7 0 5{DAG n4\`hankel`}}{INP_R 8 0 "> "{TEXT 0 14 "# \+
read hankel;"}}{COM_R 9 0{TEXT 1 212 "Hankel function procedures:
\012\012        BesselH               diff/BesselH            eva
lc/BesselH\012       evalf/BesselH       expand/BesselH     simpl
ify/BesselH\015\015Also included, an implementation of expand/Bes
selY\012"}}{INP_R 10 0 "> "{TEXT 0 41 "alias( H=BesselH, J=Bessel
J, Y=BesselY ):"}}{SEP_R 11 0}{COM_R 12 0{TEXT 1 79 "Some example
s of basic formatting, evaluation, derivatives, and simplificatio
n\015"}}{INP_R 13 0 "> "{TEXT 0 15 "BesselH(1,1,r);"}}{OUT_R 14 0
 13{DAG (3n3\`H`,4j2x0001p4n3\`r`}}{INP_R 15 0 "> "{TEXT 0 18 "Be
sselH(1,1/2,r );"}}{OUT_R 16 0 15{DAG +5*9j2x0002/3j2x0001p2n3\`P
i`/3i2x0001p2n3\`r`pA(3n3\`sin`,2pEp5p5*Bn3\`I`p5pEpAp2p4p8pA(3n3
\`cos`p14p5pB}}{INP_R 17 0 "> "{TEXT 0 12 "H(1,-1/2,x);"}}{OUT_R 
18 0 17{DAG +5*9n3\`x`/3i2x0001j2x0002p7/3j2x0001p7n3\`Pi`p4(3n3\
`cos`,2p2pBpB*Bn3\`I`pBp7pApEp4p2p4(3n3\`sin`p14pBpB}}{INP_R 19 0
 "> "{TEXT 0 18 "H( 1, -3, r^2+4 );"}}{OUT_R 20 0 19{DAG +3(3n3\`
H`,4j2x0001j2x0003+5*3n3\`r`j2x0002p5j2x0004p5i2x0001}}{INP_R 21 
0 "> "{TEXT 0 14 "H(2,-2,1+2*I);"}}{OUT_R 22 0 21{DAG (3n3\`H`,4j
2x0002p4+5j2x0001p8n3\`I`p4}}{INP_R 23 0 "> "{TEXT 0 24 "diff( H(
 1,4/3,r ), r );"}}{OUT_R 24 0 23{DAG +5(3n3\`H`,4j2x0001/3p5j2x0
003n3\`r`p5*5pBi2x0001(3p2,4p5/3j2x0004p9pBp5/3i2x0004p9}}{INP_R 
25 0 "> "{TEXT 0 29 "diff( H( 1,1/3,exp(r) ), r );"}}{OUT_R 26 0 
25{DAG *5+5(3n3\`H`,4j2x0001/3j2x0004j2x0003(3n3\`exp`,2n3\`r`i2x
0001*5pDp13(3p3,4p6/3p6pBpDp6p1Cp6pDp6}}{INP_R 27 0 "> "{TEXT 0 
14 "simplify( \" );"}}{OUT_R 28 0 27{DAG +3*5+5*5(3n3\`exp`,2+3n3
\`r`i2x0001j2x0001(3n3\`H`,4pD/3pDj2x0003(3p5,2p9pDpD(3p10,4pD/3i
2x0002p16p18i2x0003pDp18pD/3pBp16}}{INP_R 29 0 "> "{TEXT 0 11 "ev
alc( \" );"}}{OUT_R 30 0 29{DAG +5*5+5*5(3n3\`exp`,2+3n3\`r`i2x00
01j2x0001(3n3\`J`,3/3pDj2x0003(3p5,2p9pD/3pBp15(3p10,3/3i2x0002p1
5p17pDpDp17pDpD*7n3\`I`pD+5*5p4pD(3n3\`Y`p12pDp1C(3p35p21pDpDp17p
DpD}}{SEP_R 31 0}{COM_R 32 0{TEXT 1 59 "A few floating point calc
ulations with different precision\015"}}{INP_R 33 0 "> "{TEXT 0 
45 "evalf( H( 1,1,2 ) ); evalf( H( 1,1,2 ), 20 );"}}{OUT_R 34 0 
33{DAG +5e3j4x005767248078i2x0010j2x0001n3\`I`e3i4x001070324315p6
}}{OUT_R 35 0 33{DAG +5e3j6x57672480775687338720i2x0020j2x0001n3\
`I`e3i6x10703243154093754689p8}}{SEP_R 36 0}{COM_R 37 0{TEXT 1 97
 "A simple exampe to illustrate the behavior of `evalc/BesselH` w
ith general and complex arguments\015"}}{INP_R 38 0 "> "{TEXT 0 
21 "H(1,1,x); evalc( \" );"}}{OUT_R 39 0 38{DAG (3n3\`H`,4j2x0001
p4n3\`x`}}{OUT_R 40 0 38{DAG +5(3n3\`J`,3j2x0001n3\`x`p5*5n3\`I`p
5(3n3\`Y`p4p5p5}}{INP_R 41 0 "> "{TEXT 0 34 "evalf( H(1,1,1+2*I) \+
); evalc( \" );"}}{OUT_R 42 0 41{DAG (3n3\`H`,4j2x0001e3p4j2x0000
+5p6p4n3\`I`e3j2x0002p8}}{OUT_R 43 0 41{DAG (3n3\`H`,4j2x0001e3p4
j2x0000+5p6p4n3\`I`e3j2x0002p8}}{SEP_R 44 0}{COM_R 45 0{TEXT 1 81
 "A few more tests to see exactly what `simplify/BesselH` and `ex
pand/BesselH` do.\015"}}{INP_R 46 0 "> "{TEXT 0 29 "`simplify/Bes
selH`(H(2,3,x));"}}{OUT_R 47 0 46{DAG +5*5n3\`x`i2x0001+5*5p2p4(3
n3\`H`,4j2x0002j2x0001p2p10pE(3pB,4pEj2x0000p2p4p10j2x0004pAp4}}
{INP_R 48 0 "> "{TEXT 0 21 "simplify( H(2,3,x) );"}}{OUT_R 49 0 
48{DAG +3*5+7(3n3\`H`,4j2x0002j2x0001n3\`x`i2x0008*5(3p4,4p7j2x00
00pBp9pBp9j2x0004*5p3p9pBp7p9p9pBi2x0002i2x0001}}{INP_R 50 0 "> "
{TEXT 0 24 "`expand/BesselH`(2,3,x);"}}{OUT_R 51 0 50{DAG +7*5n3\
`x`i2x0002(3n3\`H`,4j2x0002j2x0001p2pCj2x0008*5p2i2x0001(3p7,4pAj
2x0000p2pCi2x0004p6p14}}{INP_R 52 0 "> "{TEXT 0 19 "expand( H(2,3
,x) );"}}{OUT_R 53 0 52{DAG +7*5n3\`x`i2x0002(3n3\`H`,4j2x0002j2x
0001p2pCj2x0008*5p2i2x0001(3p7,4pAj2x0000p2pCi2x0004p6p14}}{INP_R
 54 0 "> "{TEXT 0 28 "evalc( expand( H(2,3,x) ) );"}}{OUT_R 55 0 
54{DAG +9*5n3\`x`i2x0002(3n3\`J`,3j2x0001p2pAj2x0008*5p2i2x0001(3
p7,3j2x0000p2pAi2x0004p6p12*5n3\`I`pA+7*5p2p4(3n3\`Y`p9pAi2x0008*
5p2p12(3p28p16pAj2x0004p27pApApA}}{INP_R 56 0 "> "{TEXT 0 28 "exp
and( evalc( H(2,3,x) ) );"}}{OUT_R 57 0 56{DAG +D*5n3\`x`i2x0002(
3n3\`J`,3j2x0001p2pAj2x0008*5p2i2x0001(3p7,3j2x0000p2pAi2x0004p6p
12*7n3\`I`pAp2p4(3n3\`Y`p9pAi2x0008*7p20pAp2p12(3p26p16pAj2x0004*
5p20pAp25pApA}}{COM_R 58 0{TEXT 1 50 "NOTE: It is here that `expa
nd/BesselY` is needed.\015"}}{SEP_R 59 0}{COM_R 60 0{TEXT 1 62 "M
ost error checking is passed along to BesselJ and BesselY. .\015"
}}{INP_R 61 0 "> "{TEXT 0 12 "H(3,1/2,0.);"}}{OUT_R 62 0 61{TEXT 
2 32 "Error, (in H) invalid arguments\012"}}{INP_R 63 0 "> "{TEXT
 0 12 "H(2,1/2,0.);"}}{OUT_R 64 0 63{TEXT 2 38 "Error, (in J) sin
gularity encountered\012"}}{SEP_R 65 0}{COM_R 66 0{TEXT 1 289 "Pl
ots work as usual for complex-valued functions\015\015NOTE: I've \+
heard that future releases of Maple will have improved capabiliti
es for the plotting of complex-valued functions. Can anyone confi
rm/deny this? If not, let's exert some pressure to see\015that it
 is added to the list of additions!\015"}}{INP_R 67 0 "> "{TEXT 0
 68 "plot( \{ [ evalc(Re(H( 2, 3, x ))), evalc(Im(H( 2, 3, x))), \+
x=1..4 ],"}}{INP_R 68 0 "> "{TEXT 0 73 "           [ evalc(Re(H( \+
1, 3, x ))), evalc(Im(H( 1, 3, x))), x=1..4 ] \},"}}{INP_R 69 0 "
> "{TEXT 0 98 "           `Re`=0..0.5, `Im`=-10..10, title=`First
- and second-kind Hankel functions of order 3`);"}}{GRH_R 70 0
{RASTER 505 290 1 64 000000000000000000F833000000000000C000000000
[encoded data, 37620 characters]
00000000000000000000000000}}{SEP_R 71 0}}{END}
