ࡱ> .1+,-06bjbjss4 2 2 8|\\.T-------$03>-i-S.C$C$C$l-C$-C$C$Y_IAj[4-i.0.[p3"|3h__3,bC$--O#.32 ( Z:   Mirabilem sane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a" QP, P > Q e" 1, - GB> ?>@>6405B =5>1E>48<>5 CA;>285 ACI5AB2>20=8O ?>?0@=> ?@>AB>9 B@>9:8 $5@<0 ("$*, :0: 8 "$  ?@8<8B82=KE ?>4>189 "$* - A >1I8< <=>68B5;5<) : Z - Y = QN ?@8 N [2,"), - [3] 8 0;351@08G5A:>5 C@02=5=85 4;O Y 8;8 Z : (Y + QN)N - YN = QNPN = ZN  (Z - QN)N . @8 N = 2 @5H5=85 53> ?@54AB02;O5B A>1>9 AB0@8==K9 @5F5?B ?>;CG5=8O 2A5E >@838=0;L=KE (?>?0@=> ?@>ABKE) B@>5: 8D03>@0 ("*) : X = qp (=5GQB=K5 2708<=> ?@>ABK5), Y = ( p2  q2)/2 , Z = ( p2 + q2)/2. [4] @020O G0ABL C@02=5=8O ZN - YN = QNPN, ?>4>1=> 53> ;52>9 G0AB8, 7040NI59 CA;>285 [3] B>645AB2>< aN  bN a" (a  b)( aN-1+ aN-2b + & + bN-1), ?>4G8=5=0 2B>@><C 0;351@08G5A:><C B>645AB2C 4ab a" (a + b)2 - (a - b)2, 8 >=> ?@8 a = PN, b = QN =5GQB=KE, :0: 8 ?@8 b = QN a" 4q, :>340 GQB=> X a" QP ( 8 =5GQB=K Z, Y, N A P 87-70 Z -Y = QN), >?@545;O5B =5>1E>48<> : PNQN a" 2 - B2, - [5] $>@<C @07=>AB8 :204@0B>2 42CE F5;KE G8A5; 4;O @07=>AB8 ZN - YN . ;O X a" QP =5GQB=KE  = (PN + QN)/2, B = (PN - QN)/2,   B = QN, 2 A;CG05 65 X, Q GQB=KE  = PN + QN/4, B = PN - QN/4,   B = QN/2, 0 2 >1I5< 2845: QN = k(  B), 345 k = 2 4;O GQB=KE Q, 8=0G5 k = 1. 07=>>1@0785 7=0G5=89 N [2,") 2 [1] 2K=C6405B A>3;0A>20BL C@02=5=85 ZN - YN = PNQN A B>645AB2>< [5] 4>AB0B>G=K< 4>?>;=5=85< : PNQN a" (2 - W) - (B2 - W), [6] 345 W - DC=:F8O N 8 ?0@0<5B@>2 P, Q B0:0O, GB> 2 A>>B25BAB288 A [2] : ZN = 2 - W 8 YN = B2  W. 5>1E>48<>5 CA;>285 ACI5AB2>20=8O "$* [3] ?@8=8<05B 284 : Z  Y = QN = [2 - W)]1/N - [B2 - W)]1/N = QN 8;8 F(N,W,A,B,Q) = [2 - W)]1/N - [B2 - W)]1/N - QN = 0 [7] 4;O N [2,") A W = 0 ?@8 N = 2. 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