Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1991. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 20)

Kristyna Grytczuk: Functional récurrences and differential équations

- 31 KRYSTYNA GRYTCZUK. FUNCTIONAL RECURRENCES AND DIFFERENTIAL EQUATIONS ABSTRACT: In this paper we show connections among solutions of differential equations

, power matrices and functional recurrences. The results can be used to investigate some functional recurrences connected with number theoretic polynomi

als

. In Lhe paper CI some connections was given among solutions of differential equations of second order, power matrices and functional recurrences. We have proved the following theorem: THEOREM A. Let s

Q,t

o,u,v be functions of x and let A be a constant satisfying the following conditions: Ci) s ,t ,u

,v e C

2CJ

) where J = (x ,x )cR O O 12 Cii) u n 0, V * 0 on J and A « R

+. Then the functions y = s *u

X , y, = t -v

A J 1 O ' J 2 O are the solutions of the differential equation D y' * + D y' + D y = 0 o

J t

y 2

J where D = det o <-0 S Ü = det t t 2 O D„ = det 2 Lt S and