exact simple pole structure of eq. (\[2point\]). But one can associate the coefficients of the approximate expansion near the poles with the decay constant $f_n$ in analogy with the exact expansion shown in eq. (\[2point\]). This way one finds the masses from the localization of the poles of the two point function and the decay constants from the corresponding coefficient. That means, if $\chi_n$ are the roots of the Tricomi function: $$U (  \chi_n \,  , 0, k^2 z_0^ 2 ) = 0 \,,
 \label{roots}$$ then the holographic vector meson masses are: $$m^2_n \, =  \, 4 k^ 2  \, \chi_n \,.
 \label{new masses}$$ The decay constants are calculated numerically from the fit to the approximate form of the simple pole of eq. (\[2point\]). That means: $$f_n^ 2 \,=\, 
\lim_{p^2 \to - m^2_n} \Big( (-p^ 2)  - m_n^ 2 \Big) \, 
\Pi (p^2)   \ 
 \,.
\label{numerical decay}$$

The coupling ${\tilde g}_5 = g_5 /\sqrt{R} $ of the vector field in the AdS bulk is obtained by comparison with QCD (see refs. [@Karch:2006pv; @Grigoryan:2007my]) , wich gives: ${\tilde g}_5 \, =\, 2 \pi $.

The parameter $ k$ is flavor dependent, representing the mass of the heavy quarks. The energy scale 