Abstract
We show that solutions of the Schrödinger equation with a symmetric Pöschl-Teller potential of a particular form can be expressed in terms of a closed combination (not series) of trigonometric functions. Using some properties of the eigenfunctions of the Schrödinger equation and their inner product we determine a new exact representation of the hypergeometric function with certain values of parameters in terms of a closed combination of trigonometric functions. We also obtain new results in an explicit closed form for integrals with the hypergeometric function and with the specific combination of trigonometric functions.
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