As it is well known Butterworth and Chebyshev filters have explicit ways of calculating the order, derived by its polynomials.
For instance, for Butterworth filters:
$$ n \geq \displaystyle \frac{\log\left[\varepsilon^{-2}\left(10^{0.1A_S}-1\right)\right]}{ 2 \log \Omega_S} $$
and for Chebyshev filters
$$ n \geq \displaystyle \frac{\cosh^{-1}\left[\varepsilon^{-2}\left(10^{0.1A_S}-1\right)\right]}{\cosh^{-1} \Omega_S}$$
where, for both cases, \$ \varepsilon= \sqrt{10^{0.1A_P}-1} \$. To briefly explain the nomenclature used here: \$ A_P \$ is the passband ripple, \$ A_S \$ is the stopband attenuation and \$\Omega_S\$ is the normalized stopband frequency (the filters are normalized to a passband frequency of 1).
I was wondering if a similar approach can be taken for Bessel filters. My attempt was to consider the attenuation characteristic of the filters as:
$$A(\Omega)=10 \log \left[ \varepsilon^2C_n^2(\Omega) \right]$$
where \$C_n\$ is the \$n\$th order Bessel polynomial. I have taken a look at the Wikipedia for the Bessel polynomials, but they seem to have a complicated explicit formula, instead of a logarithm or hyperbolic cosine. Any idea on how can I predict the necessary order for a Bessel filter?