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., . .: , 1973. 297 c.
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*L [zn+c-1 (1 _ 2)i-C] = () ZC-1 (1 _ )-- F( n, Ir, C-, z). (17)



F (a, ft; ; z) = F(b, ; ; z), (18)

Ji^jr(C)Pf (a, b; ; z) =

= z"i-F(a + n+ 1, ft++; re+2; z), (19)

gi ft; c; z) =1?^5 F(a + , ft + ; + ; z), (20)

rf"

(e) z-1 F (e + , ft; c; z) = ^ Iz*+*"1 F (a, ft; c; z)], (21) 2 81 111

rf"

( ) zc'in F (a, b---z)=~n Izc"1 F (, 6; ; *)], (22)

( ) Ze-"-1 (1 z)+"-- F ( , ; ; z) =

= ' (1 - F (, 6; ; z)], (23)

(ca)(c b)n_z)a+ft-c-n F?. cz)_ (<0

= JJ K1 - z)a+ /7 (, ?:*)], (24)

()

=?1(1_"1/?('b-e; z)1, (25) (c n)n Zc-1'" (1 zf~c F (a n, 6; c n; z) =

Hn

= [z~ (1 zf-M F(a, 6; c; Z)], (26)

(e ) Zc'1 ~n (1 z)+"-" F(a n, b tr, c n; z) =

= ["1 (1 - *)+b-c /7 (a, b-, ", z)}. (27)

, :

(ic a)F(a1, b-, ; z)+(2a az-\-bz)F(a, b; ; z) +

+ a(z X)F(a+X, b-, c; z) = 0, (28)

(c b)F(a, 61; c; z) + (26 c bz + az) F(a, 6; ; z) +

+ 6(z X)F(a, b+ l; c; z)=0, (29)

c(c \){z\)F(a, b\ 1; z) + c[e 1 (2c a b l)z] F(a, 6; ; z) +

+ (c a)(c^-b)zF(a, b; e + l; z) = 0. (30)

15 (F F(a, b; ; z) /'( + ), /^ + l) F(el) F(a 1, ; ; z), F (a, b 1; ; z), F(a, 6; 1; z))

[ 2 (b a) z]F + (1 z)F(a+ \) ( )(1) = 0, (31)

( ) F + F ( +1) ^ F (6 + 1) == 0, (32)

Z)(+1) 1) = 0, (33) c[a (e b)z\Fac(\ z)F(a+ 1) +( )( b)z F (+ 1)=0, (34)

( X) F+aF(a+X) (c\)F(c\)=0, (35)

( a b)F ( a)F(a 1)+6(1- z)F(b-\- 1)=0, (36)

(6 a)(Xz)F(c a) F (a l) + (c b)F(b 1)=0, (a7)

?(1-z)F F(a l) + (c b)zF(c + 1) = 0, (38)

[<j 1 (c 6 l)z] F + te a) F (a 1) (c1)(1 z) F(c 1) = 0, (39)

[<r 2b + (6- a) z\F + b(X z)F(b +1)-^-6)/^(6-1) = 0, (40) 1SO (. 2

c[ft ( a)z]Fftc(lz)F(ft + l)-Hc )( &)/*(->=<> (41) (_?-l)f+$F(ft+l) (l)F(c-l) = 0, (42)

(1z)F/^1) + ( a)z/--(c + l)=:0, (43)

I)*]F-He-b)F(b I)( 1)(1-z)F(cl)=0, (44) [ 1 (2 ܗ I)z]F + (c )( ft)zF(c-fl)

(1)(1-a)F(e 1)=0. (45)

F(, ft; ; = (-(1)"(~)' ^0,-1,-2,..., Rec>Re(a+ft); (46)

F(a,b-,\+a ft; 1) = 2-"

'(-+O'M'

1+-ft^O,-1,-2, ...; (47) ( + 1)F(a, I; ft + 2;-I) + (6-|-l)F(->> 1; + 2; -I) =

-^????*- (48)

F(I, ; +1; - 1) = 2 [ (1 + - g)|; (49)

1 IX ( + * + )()

F(2a, 2ft; a+ ft+ ; ) = 4-h / 1 <>

a+ft + y^O, -1'-?...;

1\ (6)()

Ffrl-g ft;-1=2^ 6*0,-1,-2,...; (51)

F^al 2ft; a + ft+1; ^ =

= /( + & + 1) f_1___1 \ (52)

' (r<a)r(ft + j) { + )())'

a+ft +I :^0, -U-2, ...;

4\

-V 1 , 3 1\ /8\8 * 1) I2" + ?)

+ -1,-2..... 2.9j

/ 1 1, /8\- (2 + )(

2^ + ^0,-1,-2,..., (54)

.

f^ + i ; 2 + |-;3) =

-a.*-.-**+

(55)



pU + i. ; 2+ \i "*) =



''

2+ --^fe 0, 1,2,

2.9. 24

U1=Pia, Ir, ; )= (1)

==(1 -Zf-O-bFic-, ; ; )= (2)



= (l-z)-a F (, e-b-, , ^t)= (3)

=(1-^^--1,?^), (4)

us = P(, Ir, ++1 ; 1 )= (5)

= 1~( + 1, 6 + 1; + + 1 ; 1)= (6)

= Z-aFia, + 1 ; a+b+l , I-Z-1)= (7)

= - + \, Ir, ++1 , I-Z-1), (8)

,=( ZTaFio, + 1 ; +\ \ '1)= (9)

= ( z)-c (I-Z)c^b Fil-b, c b; a + \b-, sr1)= (10)

= O-ZTaFla, e-b-, +1-ft; (I-Z)"1]= (11) = (- z)1- (1 - z)^-' F [a +1 , 1 Ir, a + 1b; (1zT\ (12)

4=( * + \, Ir, ?+1-; z-1)= (13)

= ( zf~c (1 z)c'a~b F (I , a; b+l a, '1)= (14) IW ר [.2

= (1 z)~b F [, a; 6+1 ; (1 z)-'] = (15)

= ( zy-c (I-Z)^6-1 F [b + 1 , 1-; b + 1 , (1)'1], (16)

B6 = Z1-cFja + 1 , b + 1 ; 2 ; z) = (17)

= Z1-cO- z)c-a~b F(1-, 16,2 ; z)= (18)

= 2'-(1 zf-ar-i F^0JrX-Ci i_ ; 2 ;

= Z1-cO-Zf-*-1 F^b+ 1-, 1 ; 2 ;(20)

= (1 Zf-a^b F(e , ; +1 6; 1z)= (21)

= Z1-cO-Zfa^b F (I , 16; +1 6; 1 z)= (22)

= za~c (1 z)^-6 F ( , 1 ; + 1 6; 1 z"1) = (23)

= &_(1 Zf-a^b F( 6, 1 6; + 1 6; 1"1). (24)

Btl ..., U8 . ,

( + 6+1-)

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

- () + ( +1 ) (

( + 6+1-) 2

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

- () + (6 +1 ) *' (>) (I-A)a (6)(-6) I ^,,-.(1-)

( + 1 6) () (6+1 a)"4' (6 + 1-)() _ ( + 6 + 1 )
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