Series representation for the Jost solution of the Sturm-Liouville equation in impedance form

The Sturm-Liouville equation -1/p(x) d/dx ( p(x) du/dx) = lambda u, x epsilon (0, infinity), lambda epsilon C, is studied. The characterization of the spectral data for (SL) with the boundary condition u'(0) - hu(0) = 0, h epsilon R, is given. A series representation for the Jost solution is obtained in the form of a power series with respect to the parameter z = 1/2 +i root lambda/1/2-i root lambda.The series converges in the unit disk |z| < 1 and leads to an explicit representation for spectral data and analytic method for their computation.

Automated summary

The Sturm-Liouville equation is studied in this article, focusing on the characterization of spectral data and the solution with a specific boundary condition. The Jost solution is represented by a power series with a parameter, and this representation provides an explicit expression for spectral data and an analytic method for computation.