A Gamma Program

The factorial function (n!) (1*2*3 …*x) accepts only positive integers. Gamma, a higher transcendental function,(Γ) bears the relationship to the factorial by Γ(x)=n!(x-1), but accepts decimal and negative arguments as well. It is much used in the solution of statistical and engineering problems. First GOTO 340, then GOTO 5.

POKE 65411,64 to create gamma character (Γ) on graphics (F).

   5 PRINT "GAMMA": REM GAMMA
  10 INPUT "PAUSE PERIOD?";G
  20 INPUT "X?";X
  30 IF X=0 THEN GO TO 320
  40 IF X<0 THEN GO TO 60
  50 IF X=INT X THEN GO TO 520
  60 IF X=INT X THEN GO TO 320
  70 LET Y=INT X
  80 LET Z=X-(INT X)
  90 LET W=Z+(A*(Z↑2))+(B*(Z↑3))
+(C*(Z↑4))+(D*(Z↑5))+(E*(Z↑6))+(
F*(Z↑7))+(H*(Z↑8))+(I*(Z↑9))+(J*
(Z↑10))+(K*(Z↑11))+(L*(Z↑12))
 100 LET W=W+(M*(Z↑13))+(N*(Z↑14
))+(O*(Z↑15))+(P*(Z↑16))+(Q*(Z↑1
7))+(R*(Z↑18))+(S*(Z↑19))
 110 LET T=1/W
 120 IF Y>0. THEN GO TO 150
 130 IF X<0 THEN LET Y=ABS Y: LE
T V=Y: GO TO 190
 140 LET T=1/W: GO TO 230
 150 FOR U=0 TO Y-1
 160 LET T=T*(Z+U)
 170 NEXT U
 180 GO TO 230
 190 FOR U=1 TO Y
 200 LET T=T/(Z+(U-1))
 210 NEXT U
 220 IF V=0 OR V/2<>INT (V/2) TH
EN LET T=T*(-1)
 230 PRINT "GAMMA ";X;"=",T
 240 IF X=INT X THEN PAUSE G: CL
S : GO TO 20
 250 LET T$=STR$ T
 260 IF T$(1)="." THEN LET Z=4:
LET W$=" ": IF X<0 THEN LET W$="
"
 270 IF T$(2)="." THEN LET Z=4:
LET W$=" ": IF X<0 THEN LET Z=Z+
1: LET W$=" "
 280 IF T$(2)<>"." THEN LET Z=4:
 LET W$="  ": IF X<0 THEN LET Z=
Z+1: LET W$=" "
 290 IF ABS INT X>=4 THEN LET W$
=""
 295 IF ABS INT x=4 THEN LET w$=
" "
 300 LET Y=VAL T$(1 TO Z)
 310 PRINT ,W$;(T-Y)+.0000000008
: PAUSE G: CLS : GO TO 20
 320 PRINT "GAMMA ";X;"=","INFIN
ITY": PAUSE G: CLS : GO TO 20
 330 STOP
 340 LET A=.5772156649
 350 LET B=-.6558780715
 360 LET C=-.0420026350
 370 LET D=.1665386113
 380 LET E=-.0421977345
 390 LET F=-.0096219715
 400 LET H=.0072189432
 410 LET I=-.0011651675
 420 LET J=-.0002152416
 430 LET K=.0001280502
 440 LET L=-.0000201348
 450 LET M=-.0000012504
 460 LET N=.0000011330
 470 LET O=-.0000002056
 480 LET P=.0000000061
 490 LET Q=.0000000050
 500 LET R=-.0000000011
 510 LET S=.0000000001
 520 LET T=1
 530 FOR U=1 TO (X-1)
 540 LET T=T*U
 550 NEXT U
 560 GO TO 230