The numerical integration of dual hankel transformation

Due to strong oscillation and slow decay of product term in dual Bessel integration,it is difficult to use ordinary numerical method for the quadrature of dual Bessel.In this paper we divide [0,∞) into [0,λ₀] and [λ₀,∞);In [λ₀,∞),the integration can be written as Fourier cosine and sine transformation by asymptotic expression of Hankel Function and it can be evaluated by fast algorthm.In [0,λ₀],the integration can be computed accurately through direct quadrature.But when we calculate a quantity the related dual Bessel integration with common argument,the algorithm mentioned above seem not to be efficient enough.In this case,according to derivative relation of Bessel function,the constant transformation of the integration in [0,λ₀] can be done and the changed into the integration of the Bessel function itself which can only be calculated only once.This algorithm has improved efficiency of calculation obviously for dual Bessel integration.