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On the canonical solution of indefinite problem with \(m\) turning points of even order. (English) Zbl 1122.34020

An infinite product representation is provided for the characteristic function \(C(b,\lambda)\) of the boundary value problem
\[ y''+(\lambda p(x)-q(x))y=0,\; x\in (0,b), \]
\[ y'(0)=y(b)=0, \]
where \(p(x)\) has a finite number of zeros on \((0,b)\).

MSC:

34B24 Sturm-Liouville theory
34B05 Linear boundary value problems for ordinary differential equations
47E05 General theory of ordinary differential operators
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