Wronskian relation

The Wronskian relation (3.17) combined with (4.13,14) gives the final relation needed ... 

The first of these, which connects the logarithmic derivatives of the spherical Bessel and Neumann functions, is a direct consequence of the Wronskian relation nj - jn = S [5.4], while the latter may be derived quite generally in analogy to (4.17), to which it reduces when the two boundary conditions are - i - 1 and . In addition, we renormalise the structure constants... 

To determine the interplay between the spectral properties, both boundary conditions, we return to Weyl s theory [32]. The key quantity in Weyl s extension of the Sturm-Liouville problem to the singular case is the m-function or ra-matrix [32-36]. To define this quantity, we need the so-called Green s formula that essentially relates the volume integral over the product of two general solutions of Eq. (1), u and v with eigenvalue X and the Wronskian between the two solutions for more details, see Appendix C. The formulas are derived so that it immediately conforms to appropriate coordinate separation into the... 

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