Marasi, H. R. (2011) *Asymptotic form and infinite product representation of solution of second order initial value problem with a complex parameter and a finite number of turning points.* Հայաստանի ԳԱԱ Տեղեկագիր. Մաթեմատիկա, 46 (4). pp. 57-76. ISSN 00002-3043

## Abstract

The paper studies the differential equation yn + (р2ф2(х ) - q(x)) y = 0 (*) on the interval I = [0, 1], containing a finite number of zeros 0 < x1 < X2 < ... < < xm < 1 of ф2 , i.e. so-called turning points. Using asymptotic estimates from [6] for appropriate fundamental systems of solutions of (*) as \p\ →∞ <x, it is proved that, if there is an asymptotic solution of the initial value problem generated by (*) in the interval [0,x1 ) , then the asymptotic solutions in the remaining intervals can be obtained recursively. Furthermore, an infinite product representation of solutions of ( * ) is studied. The representations are useful in the study of inverse spectral problems for such equations.

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