Специальные функции. Мицик М.Ф. - 6 стр.

UptoLike

ВУЗ: 

ИСОиП ДГТУ | Шахты

Составители: 

Рубрика: 


0
xx
<
<ξ
, ,
( )
0≠ξz
. 
0
>
α


( ) ( )
( )
( )
−+=
α
α
α
α
ξα
2
0
2
12
1
2 x
x
xz
xzC
xzxCxu
. (12)

0
=
α
, 
( ) ( )
( )
+=
x
x
z
C
Cxzxu
0
2
12
ln
ξ
. (13)
(12) (13) , 
( )
∞→xu
2

0
→
x
.
 4.      

∞
→
:
( ) ( )
,cos
x
A
~ ϕ+xxy
(14)

A

−
ϕ
.
,  , ,    
  ,    
∞
→

π
.
.

x
z
y =
(15)
 (7) :
.0
4
1
1
2
2
=
−
−+
′′
z
x
z
ν

∞
→
, 

22
4
1
−
− xν
, :
.0
=
+
′
′
zz

() ( )
ϕ+xxz cosA~
, ,    (15) 
( )
xy
, 
 (14).
. 2, 3, 4 
 .    
         x < ξ < x0        ,                                 , z(ξ ) ≠ 0 .   α >0

                                       C z( x)  1     xα 
            u2 (x ) = C1 x z(x ) +
                                 α
                                                 α − 2α  .
                                      2α z (ξ )  x
                                           2
                                                       x0                                (12)

         α = 0,
                                             x 
            u2 (x ) = z(x ) C1 + 2 ln 0  .
                                       C
                                    z (ξ ) x                                            (13)

    (12) (13)         ,      u2 ( x ) → ∞         x → 0.
                    4.
                                                    x→∞:
              y( x ) ~        cos(x + ϕ ),
                           A
                                                                                          (14)
                            x
     A    ϕ−                                                    .
               ,                           ,             ,
                                               ,                                          x→∞
              π.
                    .

                                                   z
                                     y=                                                   (15)
                                                    x
                               (7)                              :
                                                   1
                                            ν − 
                                                2

                                     z′′ + 1 −     4 z = 0.
                                                x 
                                                  2
                                                     
                                                     
                                                                                      x→∞,
                                      2 1  −2
                                     ν −  x                                  ,          :
                                            4
                                     z′′ + z = 0 .

                        z( x) ~ A cos ( x + ϕ )
,                    ,                                              (15)       y( x ) ,
                   (14).
                     .                         2, 3, 4
                                       .

Страницы