The solution of a new kind of integrals of bessel functions used in the power calculation

Abstract

In the evaluation of the power flow in some millimeter RF structures, a new kind of integrals of the type \(\int {^r } [A\zeta _\nu (kr) + B\zeta _{ - \nu } (kr)][A'\zeta _\nu (kr) + B'\zeta _{ - \nu } (kr)]\frac{{dr}}{r},\) in which ζ±ν(kr) denotes arbitrary Bessel functions of real order ±ν, is met. In order to integrate it, a new transformation of modified Bessel function is build in this paper: then a general integral formula involving the products two terms, each of them can be expressed a sum of any two modified Bessel function, is obtained by means of applying a theorem on calculus to this transformation smartly, Furthermore, making use of the characteristics of modified Bessel function and the definition of Bessel function, the analytical expression of the above integral is derived.