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- .

., . .: , 1973. 297 c.
( ): visshietranscefunciit11973.djvu
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_(+1-.)(1-) .(+1_)

~ (2 ) ( + 1 6)

eiztc~a> T(c-a)T(l-b) _ ()(-) , (1-6)<)

( + 1 6) - () ( + 1-6)"3'

( + 6 + 1 )

_( + 1-)(1-) .(+1_) (6)(1 )

- (2-) + (6 + 1 ) (du)

(+1 )

_(1-6)(6+1-) ..-,(-)(6 + 1-)

- (2 ) (6+1-) 4' ( ' 2.9J 115

>141 )( ft)

''"i^rWi=

_ (1-)( + 1-) n_at T(c-b)T(Q + l-c)

- (2 ) + (a +1 b) (Sl)

() ( b) ()( + -) _ Ul-T(c-a)T(c-b)Us+ () ()

_()(-) () (-ft) " (-)() + ( ?) () "4'

( + 1)< + 1 ) "1+-()(6)-(<)

- r(ft+l-c)r(ft) (+1 )() '

_ (1)(+1) _ () (1 ) (a -f-1 ft) _ 7)

" X1 (1 ft) ( + 1 ) (2 ) ( ft) () ( '

r(g+l-a-ft)r(g + ft-c)r(a + l-ft) _

- (1 ft)T(e ft)r(e + ft + l-t) * " w

T(a + b-c)T(a+l-b) _6 ( -)- 1 ) T () 6 ""

r(l-c)r(l+ft-a) ()(1-)(+\-) { _

(1 )(1 -)-ft ) 1 (2 ) ( ) (ft) * b~ W -r(C + l-a-ft)r(a + ft-g)r(ft + l-a) Jltft _ ~ (1 )( a)r(a-|-ft-|-l ) '

r(a + ft-C)r(ft+l-a)

r(ft-|-1 )(6) * U (4U)

(2-)(--) (2 e) (a -j- ft )

(1)(1ft) "8+r(a+l-c)r(ft + l-c)Ue_ ^1'

- (2-) (ft-) (2-) (a-ft) -.. )

(1 ) (ft I ) 8 + (1 ft) ( 1 ) "4> ( '

(+\--)(\-) (+1 1)_____

~~ F(1 ) (1 ft) ( ) ( ft) "5 ~ W

r(c+l.-a-ft)r(ft-a)-'" +

(1 )( )

(44)

(1 ft) ( ft) *

a, ft, , -, , , ) , Im >0. , U1, , ..., , . (< , D, , 1SO (. 2

D', D-. .

lmz<0, (25)-(44) .

2.10.

, 1 , b (. 2.9(1)-2 9(4) 2.9(3)-2.9(44))

F{a, Ir, ; z) = A1Fial Ir, + ? +1; 1)+

+ (1 Zf-^-bFic-, 1, + 1 z), (1)

j arg (1 z)| <; F(a, Ir, c, z)=B,( z)-*Fia, 1 c + ar, 1 b+cr, 1) +

+ Ba - Zfb 1- + ; \-a + b\ zr>). (2)

1 arg ( z)|<*;

F(a, Ir, , z) = B1 (1 )-"F[e, e-b-, a ?+1; (1 1] +

+ Bail-z)-bF[b, c~a; * e + 1; (I-z)-1, (3)

|arg(l)|<; Fia, Ir, c, Zy=AlSTaFiat + 1, +J+l e; I zrl) +

+ AiZa-'(1 Zfa41 Fic-a, 1 er, e+l ab; 1z~l), (4)

I arg z I < .

A1, As, B1 Bi :

- ()(-) . ()( + ^-)

( ) ( ) ' 2 ()(?)

(5)

()(-) - _()(-)

0)( ) ' ѿ~()( b)'

F(, Ir, ; ) = ֗z)~a fU cb; ; , ;

()

F (, ; , ) ( /, , )

( )~~ (aWd-t+aWm ^n-, , , ( a) Z \ (+)!-^"[to(-Z) + A] +

= 0

Ttl 1

+-* I -1-^

= 0

<arg(z)<*, ; ˄ = <]>(1 + + ) + (1 + ) ( + /+) + ( ) = |/(1 + + ) + ( + ) + ( + + ) (1 + + + ) +

+ ctg ((-)], (8) 2 10] 117

F(a, +m; a + m + /+l; z)-

1 = 0 ,

( + /) _

( + + /+1)



=(-^(-^- 2 (g)"|"+m)u71)! *-" +

^+l

- 1

, V (--1)

+ ( ' L ( + / )1 ! ^ +

= 0

I (-*-"1 (^(-W-Qff47, [1, - . (9>

+ (/ + m)i Z ( + )1 [1( 2) + ɻ!' w

=

< arg (z)<w;

Ai = lKl + + n) + 4-(1 + )-( + + ) 4-(/ + 1 -), (10)

f(n + l, + + 1; + + / + 2; z) =

__ ( + + / + 1)1 (- 1)'* d f ^ rf' (1 - )

~~ !( + )!( + /)! dz^T ' dz*L * JP v ' 1

F(a, Ir, + ft + m; z)

( + * + )--1

rW - ,

(+)( + ) ^ (1-)! 11 +

=

(1 2Y1 ( 1" (a + m)(ft + m) , ,

+ ()0) Z ( + )1 !-[A-In(l-z)l(l-Z^ (12)

=

< arg(1 z)<, , fc 1, 2,...;

= + ( + 1) + + ( + +1)-'ʫ + + ')-'* + + ), (13) ߻-T

2 0 ,

? = Q

- 1

_ () (1 z)~m ()( ) - T(a)T(b) Zia (1 /) ! +



, (-1 ) -. , 1/1 /t,4

+ ( m)T(b m) Z ( + )! 1 - In (1 - z)] (1 - z), (14)

n =SS

arg(lz)<it, a, b, ,1,2,..,; 1SO
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