Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1993. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 21)

Krystyna Grytczuk: Effective integrability of the differenctial equation ...

(26) iL PJ-S jj = 0. j — 0 Thus we obtain that the condition (6) of the Theorem 2 satisfied. Therefore by the Theorem 2 our Corollory 1 follows. Corollary 2. Let the function y 0 = Ts 0 k- u k be a solution of (1) and let A be the matrix of the form: ín n n A = Z... ^0,1 *r=l Jt=l n,l V «-1,1 n-\,n 0.« / Moreover let D h J._ } denote the minor of the matrix A which we obtain by deleting the first row and j column for j = 1,2,...,« +1. Then in the differenctial equation (1) we can take Pj-M-ir 1^ Proof. From the Theorem 1 we obtain / n <t (27) fjis^»; SVu«i =0 Since y„ = £ .v„ k u^ * 0 on ./ thus by (27) we have k= 1 (28) P x s nj c • < J+- • • • +P n_ x ^ Z • < 101

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