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- *DECK BESI0E
- FUNCTION BESI0E (X)
- C***BEGIN PROLOGUE BESI0E
- C***PURPOSE Compute the exponentially scaled modified (hyperbolic)
- C Bessel function of the first kind of order zero.
- C***LIBRARY SLATEC (FNLIB)
- C***CATEGORY C10B1
- C***TYPE SINGLE PRECISION (BESI0E-S, DBSI0E-D)
- C***KEYWORDS EXPONENTIALLY SCALED, FIRST KIND, FNLIB,
- C HYPERBOLIC BESSEL FUNCTION, MODIFIED BESSEL FUNCTION,
- C ORDER ZERO, SPECIAL FUNCTIONS
- C***AUTHOR Fullerton, W., (LANL)
- C***DESCRIPTION
- C
- C BESI0E(X) calculates the exponentially scaled modified (hyperbolic)
- C Bessel function of the first kind of order zero for real argument X;
- C i.e., EXP(-ABS(X))*I0(X).
- C
- C
- C Series for BI0 on the interval 0. to 9.00000D+00
- C with weighted error 2.46E-18
- C log weighted error 17.61
- C significant figures required 17.90
- C decimal places required 18.15
- C
- C
- C Series for AI0 on the interval 1.25000D-01 to 3.33333D-01
- C with weighted error 7.87E-17
- C log weighted error 16.10
- C significant figures required 14.69
- C decimal places required 16.76
- C
- C
- C Series for AI02 on the interval 0. to 1.25000D-01
- C with weighted error 3.79E-17
- C log weighted error 16.42
- C significant figures required 14.86
- C decimal places required 17.09
- C
- C***REFERENCES (NONE)
- C***ROUTINES CALLED CSEVL, INITS, R1MACH
- C***REVISION HISTORY (YYMMDD)
- C 770701 DATE WRITTEN
- C 890313 REVISION DATE from Version 3.2
- C 891214 Prologue converted to Version 4.0 format. (BAB)
- C***END PROLOGUE BESI0E
- DIMENSION BI0CS(12), AI0CS(21), AI02CS(22)
- LOGICAL FIRST
- SAVE BI0CS, AI0CS, AI02CS, NTI0, NTAI0, NTAI02, XSML, FIRST
- DATA BI0CS( 1) / -.0766054725 2839144951E0 /
- DATA BI0CS( 2) / 1.9273379539 93808270E0 /
- DATA BI0CS( 3) / .2282644586 920301339E0 /
- DATA BI0CS( 4) / .0130489146 6707290428E0 /
- DATA BI0CS( 5) / .0004344270 9008164874E0 /
- DATA BI0CS( 6) / .0000094226 5768600193E0 /
- DATA BI0CS( 7) / .0000001434 0062895106E0 /
- DATA BI0CS( 8) / .0000000016 1384906966E0 /
- DATA BI0CS( 9) / .0000000000 1396650044E0 /
- DATA BI0CS(10) / .0000000000 0009579451E0 /
- DATA BI0CS(11) / .0000000000 0000053339E0 /
- DATA BI0CS(12) / .0000000000 0000000245E0 /
- DATA AI0CS( 1) / .0757599449 4023796E0 /
- DATA AI0CS( 2) / .0075913808 1082334E0 /
- DATA AI0CS( 3) / .0004153131 3389237E0 /
- DATA AI0CS( 4) / .0000107007 6463439E0 /
- DATA AI0CS( 5) / -.0000079011 7997921E0 /
- DATA AI0CS( 6) / -.0000007826 1435014E0 /
- DATA AI0CS( 7) / .0000002783 8499429E0 /
- DATA AI0CS( 8) / .0000000082 5247260E0 /
- DATA AI0CS( 9) / -.0000000120 4463945E0 /
- DATA AI0CS(10) / .0000000015 5964859E0 /
- DATA AI0CS(11) / .0000000002 2925563E0 /
- DATA AI0CS(12) / -.0000000001 1916228E0 /
- DATA AI0CS(13) / .0000000000 1757854E0 /
- DATA AI0CS(14) / .0000000000 0112822E0 /
- DATA AI0CS(15) / -.0000000000 0114684E0 /
- DATA AI0CS(16) / .0000000000 0027155E0 /
- DATA AI0CS(17) / -.0000000000 0002415E0 /
- DATA AI0CS(18) / -.0000000000 0000608E0 /
- DATA AI0CS(19) / .0000000000 0000314E0 /
- DATA AI0CS(20) / -.0000000000 0000071E0 /
- DATA AI0CS(21) / .0000000000 0000007E0 /
- DATA AI02CS( 1) / .0544904110 1410882E0 /
- DATA AI02CS( 2) / .0033691164 7825569E0 /
- DATA AI02CS( 3) / .0000688975 8346918E0 /
- DATA AI02CS( 4) / .0000028913 7052082E0 /
- DATA AI02CS( 5) / .0000002048 9185893E0 /
- DATA AI02CS( 6) / .0000000226 6668991E0 /
- DATA AI02CS( 7) / .0000000033 9623203E0 /
- DATA AI02CS( 8) / .0000000004 9406022E0 /
- DATA AI02CS( 9) / .0000000000 1188914E0 /
- DATA AI02CS(10) / -.0000000000 3149915E0 /
- DATA AI02CS(11) / -.0000000000 1321580E0 /
- DATA AI02CS(12) / -.0000000000 0179419E0 /
- DATA AI02CS(13) / .0000000000 0071801E0 /
- DATA AI02CS(14) / .0000000000 0038529E0 /
- DATA AI02CS(15) / .0000000000 0001539E0 /
- DATA AI02CS(16) / -.0000000000 0004151E0 /
- DATA AI02CS(17) / -.0000000000 0000954E0 /
- DATA AI02CS(18) / .0000000000 0000382E0 /
- DATA AI02CS(19) / .0000000000 0000176E0 /
- DATA AI02CS(20) / -.0000000000 0000034E0 /
- DATA AI02CS(21) / -.0000000000 0000027E0 /
- DATA AI02CS(22) / .0000000000 0000003E0 /
- DATA FIRST /.TRUE./
- C***FIRST EXECUTABLE STATEMENT BESI0E
- IF (FIRST) THEN
- NTI0 = INITS (BI0CS, 12, 0.1*R1MACH(3))
- NTAI0 = INITS (AI0CS, 21, 0.1*R1MACH(3))
- NTAI02 = INITS (AI02CS, 22, 0.1*R1MACH(3))
- XSML = SQRT (4.5*R1MACH(3))
- ENDIF
- FIRST = .FALSE.
- C
- Y = ABS(X)
- IF (Y.GT.3.0) GO TO 20
- C
- BESI0E = 1.0 - X
- IF (Y.GT.XSML) BESI0E = EXP(-Y) * ( 2.75 +
- 1 CSEVL (Y*Y/4.5-1.0, BI0CS, NTI0) )
- RETURN
- C
- 20 IF (Y.LE.8.) BESI0E = (.375 + CSEVL ((48./Y-11.)/5., AI0CS, NTAI0)
- 1 ) / SQRT(Y)
- IF (Y.GT.8.) BESI0E = (.375 + CSEVL (16./Y-1., AI02CS, NTAI02))
- 1 / SQRT(Y)
- C
- RETURN
- END
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