Reduction of algebraic integrands involving universal functions. Application to Sundman-type transformations in orbital motion (Q5926723)

The author considers a universal formulation of two-body problem (valid for any kind of conic sections) in which the main dynamical parameters depend on Battin universal functions \(U_{0}, U_{1}\) and \(U_{2}\) defined as NEWLINE\[NEWLINE U_{n}(s,\rho)=\sum_{k=0}^{\infty}(-1)^{k}\rho^{k}s^{2k+n}/(2k+n)!\;. NEWLINE\]NEWLINE A change of integration variable is performed in order to reduce integrands containing transcedental universal functions to integrands containing polynomials. The method is applied to the Keplerian motion with moderate anomaly.