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We present new asymptotic series for the Legendre and Jacobi functions of thefirst and second kinds in terms of Bessel functions with appropriate arguments.The results are useful in the context of scattering problems, improve on knownlimiting results, and allow the calculation of corrections to the leadingBessel-function approximations for these functions. Our derivations of theseseries are based on Barnes-type representations of the Legendre, Jacobi, andBessel functions; our method appears to be new. We use the results, finally, toobtain asymptotic Bessel function expansions for the rotation functions neededto describe the scattering of particles with spin.

Asymptotic Bessel-function expansions for Legendre and Jacobi functions