Специальные функции. Мицик М.Ф. - 3 стр.

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(
)
(
)
+∞
=
Γ
=
Γ
∞→+→
xx
xx
limlim
0
.
   
(
)
(
)
121 =Γ=Γ
,  
(
)
xΓ
 

(
)
2;1
.  1.
 Maple 9.5.
 1. .
 (6)  (1) 
0
>
x
,
  
0
<
x
,  (1) . 
 (6)    
0
<
x
  
,...3,2,1,0
−
−
−
=
x
.   (6)   
     
.
 (6) , 
(
)
−∞
=
Γ
−→
x
x 0
lim
.
 ,  (1) (6)    -

,...3,2,1,0
−
−
−
=
x
, 
( )
−∞
−∞±
=Γ
±−→
.,
;,
lim
0
n
n
x
nx
m
  « »   

(
)
xΓ

∞
→
x
( )
+==+Γ
−
∞
−
∫
x
Oxxedtetx
xxtx
1
121
0
π
.
              lim Γ( x ) = lim Γ( x ) = +∞ .
              x →+0                  x→∞

                                 Γ(1) = Γ(2 ) = 1 ,                                  Γ( x )
               (1;2) .                                                                         1.
                                                                                              Maple 9.5.




                                              1.                                     .

                    (6)                                                              (1)              x > 0,
                      x < 0,                             (1)                     .
                   (6)                                               x<0
x = 0,−1,−2,−3,... .                                               (6)

          .
                           (6)                ,
                                     lim Γ ( x ) = −∞ .
                                     x→ − 0

                                 ,                 (1)    (6)                                              -
                         x = 0,−1,−2,−3,... ,
                                 ± ∞,         n−                        ;
               lim Γ( x ) = 
              x→ − n ± 0
                                m ∞,         n−                             .
              «                                                »
                  Γ( x )             x→∞
                                 ∞
                                                                1 
              Γ( x + 1) = ∫ t x e −t dt = e − x x x 2π x 1 + O      .
                          0                                      x 

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