Asymptotic expansions for the Bessel transformations with high oscillations by using the homotopy technique.

In this paper, we establish the asymptotic expansions for the integration containing the Bessel functions with high oscillations by using the homotopy technique. The proposed method is constructed by approximating the non-oscillatory or low-oscillatory factor in practice. Two cases are considered, that is, the case 0 [image omitted] [a, b] and the case 0∈[a, b], where [a, b] denotes the integration interval. The efficiency of the technique and the correctness of the theory are shown by several examples. [ABSTRACT FROM AUTHOR]