A note on the asymptotics of the modified Bessel functions on the Stokes lines

R Paris
2017 Mathematica Aeterna   unpublished
We employ the exponentially improved asymptotic expansions of the confluent hypergeometric functions on the Stokes lines discussed by the author [Appl. Math. Sci. 7 (2013) 6601-6609] to give the analogous expansions of the modified Bessel functions I ν (z) and K ν (z) for large z and finite ν on arg z = ±π (and, in the case of I ν (z), also on arg z = 0). Numerical results are presented to illustrate the accuracy of these expansions. Mathematics Subject Classification: 30E15, 33C10, 34E05, 41A60
fatcat:xztbbmufyranvbxzaiu6qkhk3u