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A specific Sturm-Liouville differential equation

Explicit solutions of the second order ordinary differential equation y′′(x)+(λ+12 sech2x)y(x)=0 and its eigenpairs are obtained by calculating complex residues. Eigenpairs (energey states and energy function), spectral function and eigenfunction expansions are also reported.
PAPER REVISED: 2018-10-08
PAPER ACCEPTED: 2018-10-27
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