Abstract
Consider the general fourth order case where the coefficients a (1)j and (3)j are subject to the conditions (10) i.e.
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In cases (v) and (vi) split the diagram into its upper and lower halves. Each of these halves is symmetrical. Each half represents the system of equations sk = 0. Apply the method of paragraph 5 to this system.
This may be verified by differentiating out (17) and (18) and comparing terms. As a check, note the case R ≡ 0.
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Sinden, F.W. (1954). Extensions. In: An Oscillation Theorem for Algebraic Eigenvalue Problems and its Applications. Mitteilungen aus dem Institut für angewandte Mathematik, vol 4. Springer, Basel. https://doi.org/10.1007/978-3-0348-4149-8_8
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DOI: https://doi.org/10.1007/978-3-0348-4149-8_8
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