Recently, the mutual inductance between Bitter coils with rectangular cross‐section has been calculated through Bessel function approach or figured out with analytical and semi‐analytical formulas. In this study, using the inverse Mellin transform, relevant Bessel integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the hypergeometric functions. In addition, the results obtained by this method are compared with those by finite element method software. Also, the presented approach shows great advantages of high accuracy and very short computational time.