,,,
1.
2.
2.1 -
2.2
3. -
4.
5.
, , , .
. .
:
.
- . Γ(z).
, - .
- , .
1.
-:
1. - n
(n) = (n - 1)! = 12... (n - 1). (1)
2. x>0 - .
. (2)
3. - :
(3)
1.
- (6).
:
6 , (1):
(6) =(6-1)! = 5! = 120
: 120.
2.
- (0,5).
:
(2):
.
.
: .
3.
- (1,5).
:
(3):
y = 1.5 + 2 = 3.5.
.
: .
2.
2.1 -
G(a) =(2.1)
.
1. -
=ty, t > 0 ,
G(a) =
, t 1+t ,
t 0 , :
,:
(2.2)
(2,1) ,
(2.3)
2. -
(2.4)
- , . n=1 (2.4)
2.2
- -. .
- x>0 ( z) :
.
, . g=5 n=6, , eps . , : Re z > 0.
- x>0 Gam(z+1)=z*Gam(z) Gam(z+1). , -, .
-, , ( ), -, - x, .
LnGam() - :
Ck ( 1).
k | C |
1 | 2.5066282746310005 |
2 | 1.0000000000190015 |
3 | 76.18009172947146 |
4 | -86.50532032941677 |
5 | 24.01409824083091 |
6 | -1.231739572450155 |
7 | 0.1208650973866179e-2 |
8 | -0.5395239384953e-5 |
1. Ck
- . .
3 -
- 3, 4, 5, 6.
:
- X ;
- RS ;
- GN ;
- Y ;
- RES -;
- GAM , -.
3 GAMMA
4 GAMMA_ WHOLE
5 - - GAMMA_LN
6 - - GAMMA_POINT
4.
;
(SETQ CN '(2.5066282746310005 1.0000000000190015 76.18009172947146 -86.50532032941677 24.01409824083091
-1.231739572450155 0.1208650973866179e-2 -0.5395239384953e-5))
;
(DEFUN GAMMA_LN (X)
(SETQ SER (CADR CN))
(SETQ L (CDDR CN))
(SETQ Y X)
(DO
((J 2))
((>= J 8))
(SETQ Y (+ Y 1))
(SETQ CO (CAR L))
(SETQ SER (+ SER (/ CO Y)))
(SETQ L (CDR L))
(SETQ J (+ J 1))
)
(SETQ Y (+ X 5.5))
(SETQ Y (- Y (* (+ X 0.5) (LOG Y))))
(SETQ Y (+ (* -1 Y) (LOG (* (CAR CN) (/ SER X)))))
)
; -
;
(DEFUN GAMMA (X)
(EXP (GAMMA_LN X))
)
;
(DEFUN GAMMA_WHOLE (X)
(SETQ X (- X 1))
(DO
((RES 1) (RS 1))
((EQL X 0) RS)
(SETQ RS (* RES RS))
(SETQ X (- X 1))
(SETQ RES (+ RES 1))
)
)
;
(DEFUN GAMMA_POINT (X)
(IF (> X 0)
(PROGN
(SETQ Y (+ X 2))
(SETQ GAM (* (SQRT (* 2 (/ PI Y))) (EXP (+ (* Y (LOG Y)) (- (/ (- 1 (/ 1 (* 30 Y Y))) (* 12 Y)) Y)))))
(SETQ RES (/ GAM (* X (+ X 1))))
)
;
(PROGN
(SETQ J 0)
(SETQ Y X)
(DO
(())
((>= Y 0))
(SETQ J (+ J 1))
(SETQ Y (+ Y 1))
)
(SETQ GAM (GAMMA_POINT Y))
(DO
((I 0))
((>= I (- J 1)))
(SETQ GAM (/ GAM (+ X I)))
(SETQ I (+ I 1))
)
(SETQ RES GAM)
)
)
RES)
;
(SETQ FUNC 0)
(SETQ INPUT_STREAM (OPEN " D:\GAMMA.TXT" :DIRECTION :INPUT))
(SETQ FUNC (READ INPUT_STREAM))
(CLOSE INPUT_STREAM)
; -
(SETQ OUTPUT_STREAM (OPEN "D:\RESULT.TXT" :DIRECTION :OUTPUT))
(PRINT 'RESULT_OF_GAMMA_FUNCTION OUTPUT_STREAM)
;
(PRINT (MAPCAR 'GAMMA FUNC) OUTPUT_STREAM)
;
(PRINT (MAPCAR 'GAMMA_WHOLE FUNC) OUTPUT_STREAM)
;
(PRINT (MAPCAR 'GAMMA_POINT FUNC) OUTPUT_STREAM)
(TERPRI OUTPUT_STREAM)
(CLOSE OUTPUT_STREAM)
;END
5
1.
7 . -
8 . -
2.
9 . -
10 . -
3.
11 . -
12 . -
, . , , .
. - , - , - . .
1. , .. [] / .., ... .: , 2007. 708 .
2. - - [ ] : http://www.cyberguru.ru/cpp-sources/algorithms/vytchislenie-gamma-funktsii-i-beta-funktsii.html
3. - [ ] : http://ru.wikipedia.org/wiki/_
4. , .. : . [] / .., 3- .:-, 2006. C. 412.
5. , .. . [] / .., ... .: , 2006. C. 346.
6. , .. [] / .., .., ... : , 2002. 160 .
7. , .. Lisp. [ ] / .., .. . .: , 2003. . 79.
8. . [] / ., .. .: , 1990. 460 .
1. 2. 2.1 - 2.2 3. - 4.
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