GAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR 

 X.GT.O. A RATIONAL CHEBYSHEV APPROXIMATION IS USED ON 

 8.LT. X.LT. 1000. , THE ASYMPTOTIC EXPANSION FOR X. BE. 1000. 

 A RATIONAL CHEBYSHEV APPROXIMATION ON 2. LT. X.LT. 3. FOR 

 0.LT.X.LT.8. AND X NON-INTEGRAL, FORWARD OR BACKWARD 

 RECURSION FILLS IN THE INTERVALS 0.LT.X.LT.2 AND 

 3. LT. X.LT. 8. FOR X = l . , 2. , . . . , 100. , GAMLN 13 SET TO 

 NATURAL LOGS OF FACTORIALS. 



DESCRIPTION OF ARGUMENTS 

 INPUT 



X - X.GT.O 

 OUTPUT 



GAMLN - NATURAL LOG OF THE GAMMA FUNCTION AT X 



AND 



DIMENSION GLN(IOO) ,P(5) ,Q(2) ,PC0E(9) , QCOE (4) 



, 9. 189385332047E-01/ 

 940956105200E-04/, 

 P(4)/-2.777777756577E-03/, 



Q(2)/8.333333333333E-02/ 



DATA XLIM1,XLIM2,RTWPIL/ 8. , 1000. 



DATA P(i)/7.663451880000E-04/, P(2)/-5. 



1 P(3)/7.936431104845E-04/ , 



2 P(5)/8.333333333332E-02/ 

 DATA Q(l)/-2.777777777778E-03/ 

 DATA PCOE(l) / 2. 97378664481 0E-03/,PC0E( 2) /9. 238 194559028E-03/, 



1 PC0E(3) / 1.0931 159567 10E-01/,PC0E (4) /3. 980671310204E-01/ , 



2 PC0E(5i 12. 159943128461E+00/,PC0E(6)/6.33B067999387E+00/, 



3 PC0E(7) 12. 0782472531 79E + 01 / , PCOE ( 8) /3. 603677 253002E + 01 / , 



4 PC0E<9) /6.200383S00713E+01/ 



DATA QCOE(1)/1.000000000000E+00/,QCOE(2)/-8.906016659498E+00/, 



1 QCOE (3) /9. 822521 104714E + 00/ , QCOE (4) /'6. 200383 800713E + 01/ 



DATA GLN 



I GLN 



I GLN 



; GLN 



I GLN 



j GLN 



> GLN 



' GLN 



i GLN 



} GLN 



GLN 



I GLN 



GLN 



GLN 



GLN 



GLN 



GLN 



GLN 



GLN 



H A GLN 



GLN 



GLN 



GLN 



GLN 



GLN 



(1) /O, 

 (4) /l, 

 ( 6 ) / 4 , 

 (8) /'8, 

 ( 1 ) / 1 . 

 < 1 2 ) / 1 , 

 (14) 12, 

 (16)/2. 

 ( 1 8 ) / 3 . 

 (20) /3. 

 (22)/4, 

 (24) /5. 

 (26) /5. 

 (28) / 6. 

 (30)/ 7. 

 (32i/7. 

 (34) /8. 

 (36)/9. 

 (38) /9. 

 (401/1. 

 (42) /l. 

 (44) /I. 

 (46) /l. 

 (48) /l. 

 (50) /I. 



93 



44 



, GLN(2) 



175946922 



749174278 



516136106 



018274800 



023078458 



521638531 



992713838 



050734501 



398841872 



801338984 



066755677 



036052229 



575386270 



570389671 



922235533 



544670175 



361756036 



306124547 



631760260 



034211781 



533081515 



123933639 



802722637 



565743946 



/ . / , 

 8E+00/ 



2E+00/ 

 5E+00/ 

 8E+01/ 

 7E+01/ 

 2E+01/ 

 4E+01/ 

 4E+01/ 

 OE + 01 / 

 8E+01/ 

 6E+01/ 

 8E+01/ 

 1E+01/ 

 7E+01/ 

 2E+01/ 

 8E+01/ 

 9E+01/ 

 9E+01/ 

 6E+02/ 

 5E+02/ 

 4E+02/ 

 1E+02/ 

 3E+02/ 

 3E+02/ 



GLN (3) / 

 GLN(5) 

 GLN(7) 

 GLN(9) 

 GLN(ll) 

 GLN(13) 

 GLN(15) 

 GLN(17) 

 GLNU9) 

 GLN(21) 

 GLN(23i 

 GLN(25) 

 6LN(27) 

 GLN (29) 

 GLN (31) 

 GLN(33) 

 GLN (35) 

 GLN (37) 

 GLN(39) 

 GLN (41) 

 GLN(43) 

 GLN (45) 

 GLN(47) 

 GLN(49) 

 GLN (51) 



93147180559 

 . 1780538303 

 .5792512120 

 .0604602902 

 .5104412573 

 .9987214495 

 .5191221182 

 .0671860106 

 .6395445208 

 .2335616460 

 .8471181351 

 .4784729398 

 . 1261701761 

 .7889743137 

 .4658236348 

 . 1557959456 

 . 8580827542 

 .5719694542 

 .0296819361 

 . 1032063971 

 .1777188139 

 .2531727114 

 .3295257503 

 .4067392364 

 .4847776695 



9E-01/, 

 48E+00/ 

 10E+00/ 

 74E+01/ 

 08E+01/ 

 66E+01/ 

 74E+01/ 

 OBE+Oi/ 

 03E+01/ 

 75E+01/ 

 84E+01/ 

 11E+01/ 



ooE+oiy 



18E+01/ 

 83E+01/ 

 12E+01/ 

 20E+01/ 

 14E+01/ 

 45E+02/ 

 48E+02/ 

 97E+02/ 

 94E+02/ 

 56E+02/ 

 82E+02/ 

 18E+02/ 



GLN11 

 GLN12 

 GLN13 

 GLN14 

 GLN15 

 GLN16 

 GLN17 

 GLN18 

 GLN19 

 GLN20 

 GLN21 

 GLN22 

 GLN23 

 GLN24 

 GLN25 

 GLN26 

 GLN27 

 GLN28 

 GLN29 

 GLN30 

 GLN31 

 GLN32 

 GLN33 

 GLN34 

 GLN35 

 GLN36 

 GLN37 

 GLN38 

 GLN39 

 GLN40 

 GLN41 

 GLN42 

 GLN43 

 GLN44 

 GLN45 

 GLN46 

 GLN47 

 GLN48 

 GLN49 

 6LN50 

 GLN51 

 GLN52 

 GLN53 

 GLN54 

 GLN55 

 GLN56 

 GLN57 

 GLN58 

 GLN59 

 GLN60 

 GLN61 

 GLN62 

 GLN63 

 GLN64 

 GLN65 



Figure A3. (Sheet 23 of 25) 



A27 



