Osnovy teorii Galua.

~ 5. Ypaenenuw CO 3I-1~On pemfenol-lli epyfnoiU18

185

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pey~baa '/KopaHa, KOTO~bIX Mbl 3,aecb He nHBHIOaHM.
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H4r o6bI Bblql4CJITb D, HaI4JeM 3aBHCHMOCI'b meKay BL(x) ii I1pOH3BOJV
Hott B~ '(X). HCXOai H3 aierKo HpOBepu~Mbix cpopmyn
E(x + E1~ (x), E' (x) = ()
6yJ~em HmeTb,:
B,,(x) x'~ + nB ~(x), B'(x) = n
OTK<YJaa
(5.12) B (x) = x'-H Bj (x).
O6o3Hiaga KOPHH4 ypaBHeHIH5 (5.1 1) 'iepe3 x1, x2,.., H, n4fOJCTaBBJIH
B (5.12) x = x,, noJnyqufM:
JIICKPHMHIHaHT ypaBiiHVHH1 (5.1 1) Tai(mm o6pa3om paBeH:?i(n - I
D -) 2 Bj(xl). B'i (X2). B,(x)=
k- I) (j
(5.13) D=(1) 2(n!).
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TaK( Ha3bIBaemoMv,,IOCTynlaTy IBepTpaHa", Briep~bie a1oKa3aHHomy qe6buineBbIM, BC eraa cymeLCTBYIOT 11pOCTbje 4IicJa, newaautie mewrty H~ n-, a TaKHe
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WToro fl )AOMKHO aeJ1HTbCHI Ha 4.
4. nozlmomni (5.3) To)K~e imMeOT B xaqeCTBe rpynHfbi Faiya cIimmeTpMiteCKYIO HRR Ma~eemHy rpy riy. OTHOCHTe.TbHo 9T01'O MOIKHO CKa3aTb
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MX JIMCKHMMHBaHTa D,,, BOCHOJ~b3yeMCq cJIeJ1pouiimiM COOTHoHmeHINSMH, KOTOpbje HeTPYJLHO npOBepMTb:
(5.14) xGn' (x) == nG,,(x) + n(n + 1) Gin1 (x),
(5.15) Gi, (x) ==(x - 2n) Gj,_ (x) - n(n -- 1) G 2(x).