  In this paper, we consider Klein Gordon particle near Reissner-Nordstr\"{o}m
black hole. The symmetry of such background lead us to compare the
corresponding Laplace equation with the generalized Heun functions. Such
relation help us achieve the generalized $sl(2)$ algebra and some suitable
results for describing the above mentioned symmetry. On the other hand in case
of $r\rightarrow r_{+}$ which is near the proximity black hole, we obtain the
energy spectrum and wave function. When we compare the equation of $R-N$
background with Laguerre differential equation, we show that the obtained
energy spectrum is same as three dimensional harmonic oscillator. So, finally
we take advantage of harmonic oscillator energy and make suitable partition
function. Such function help us to obtain all thermodynamical properties of
black hole. Also, the structure of obtained entropy lead us to have some bit
and information theory in the $R-N$ black hole.
