  The moments of Bessel functions and Bessel-trigonometric functions play a
basic role in many practical problems and numerical analysis. This paper
presents a complete analysis for these moments based on the recursive relations
of Bessel functions. To evaluate the moments of Bessel functions numerically, a
fast and efficient scheme is also proposed to approximate the integral of
Bessel function of the first kind and of zero order. The moments of
Bessel-trigonometric functions are proved to be expressed in a closed form. In
the numerical results, the accuracy and efficiency of the proposed analysis for
the moments of Bessel functions is validated first and then by comparing the
existing methods, a better scheme for the moments of Bessel functions is
presented.
