By Christopher Baltus, William B. Jones (auth.), Wolfgang J. Thron (eds.)
Read or Download Analytic Theory of Continued Fractions II: Proceedings of a Seminar-Workshop held in Pitlochry and Aviemore, Scotland June 13–29, 1985 PDF
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Extra resources for Analytic Theory of Continued Fractions II: Proceedings of a Seminar-Workshop held in Pitlochry and Aviemore, Scotland June 13–29, 1985
Sample text
E*) w i l l be c o n t a i n e d 1 1 + c i - Icl ~ I, and h e n c e the r a d i i p. The c o m m o n E*. ~ +~ 1 < y . PO : Jzl - R e ( z ) to by Re(c) p E* m a y be d e s c r i b e d by then E* both tend 41 Iz-[c(1+e) -p 2 +~]1 < P +~, Jz-[c(l+c) _p2 +s]t < P+£* = , where All three 3. A test We P0 o If ~, : p (1 1 + o l - l e l - 1 + ( I v ~ l - 1 ) pc ~* = p (11+ci tend of to the have an there 0 c -I + (1 - l i v ~ l ) p when c ~ as , )• described. 1) _~ r! 7). 42 where the branch of ~- is c h o s e n + 4 a + 4 r ' 2 e i 2 8 j = 1 + 2c We f i n d such that for that f -c = ~ 4a + 4 r ' e - (1 + 2c - 2r'e i6) 4[a - c ( 1 + e ) ] ,[Jl N = 4(1+2c)[ e -I 1+2c c I+c = 4 ( I + 2 c ) [ p e i8 where has r' = 0 (p = 0).
Bn_l,k(Z ) = CBn,k(Z ) where fact 3. "'" 2 we the c o e f f i c i e n t s that the h y p o t h e s i s reach Definition and 4k under order exists Thus, - u p to a c o n s t a n t In From Ak nonzero solution ~n a H ( - n + k + l ) ( c ) (-1, F 0 _ n (-1)n@0H n ~n ~ O. 1] [6]). 2] m=O by C. 2, > is In fLs SSMP shown that in occur as THEOREM 9. ) with = ~. It positive and L (C) of the Under C, namely T-fraction z a could generated {Cn}n=_ a positive with a pair fLs 2 we associated L(C) for start can a pair and M-table 0 We Definition determinants and the such to { - C _ n } n = _ ~, here.
8) r' limit). E*) w i l l be c o n t a i n e d 1 1 + c i - Icl ~ I, and h e n c e the r a d i i p. The c o m m o n E*. ~ +~ 1 < y . PO : Jzl - R e ( z ) to by Re(c) p E* m a y be d e s c r i b e d by then E* both tend 41 Iz-[c(1+e) -p 2 +~]1 < P +~, Jz-[c(l+c) _p2 +s]t < P+£* = , where All three 3. A test We P0 o If ~, : p (1 1 + o l - l e l - 1 + ( I v ~ l - 1 ) pc ~* = p (11+ci tend of to the have an there 0 c -I + (1 - l i v ~ l ) p when c ~ as , )• described. 1) _~ r! 7). 42 where the branch of ~- is c h o s e n + 4 a + 4 r ' 2 e i 2 8 j = 1 + 2c We f i n d such that for that f -c = ~ 4a + 4 r ' e - (1 + 2c - 2r'e i6) 4[a - c ( 1 + e ) ] ,[Jl N = 4(1+2c)[ e -I 1+2c c I+c = 4 ( I + 2 c ) [ p e i8 where has r' = 0 (p = 0).
