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Analytic treatment of geodesics in five-dimensional Myers-Perry space--times

We present the complete set of analytical solutions of the geodesic equation in the five-dimensional Myers-Perry space-time with equal rotation parameter in terms of the Weierstraß' elliptic and Weierstraß' zeta and sigma functions. We study the underlying polynomials in the polar and radial equations which depend on the parameters of the metric and conserved quantities of a test particle and characterize the motion by their zeros. We exemplify the efficiency of the analytical method on the orbits of test particles.