It is important to verify the homogeneity of transfer functions. The first one is not unitless unless \$k\$ has the dimension of a frequency. The way to write a transfer function is to respect a so-called low-entropy format, a term forged by Dr. Middlebrook some years ago. What it means is simply to express the formula so that you gain insight in what the expression does just by looking at it, for instance inferring from the expression if there are poles, zeroes, some gain etc. Also, you write a transfer function for a design purpose. In a bandpass filter, what matters is surely the resonant frequency but also the gain at the resonance. It is important to account for this goal when writing the transfer function. This is called design-oriented analysis or D-OA.
A transfer function should be expressed with a leading term carrying the unit or the dimension of what you want to express. If this is a gain that you write, then the leading term is a unitless term [V]/[V] or [A]/[A] for instance. If you write an impedance, then the leading term is resistance expressed in [\$\Omega\$]. This is extremely useful to check homogeneity of the formulas. In the case of a bandpass filter, a possible canonical expression is this one:
In this expression \$Q\$ is unitless and \$\omega_0\$ is expressed in rad/s. \$H_0\$ represents the gain at the resonance.
This is truly the most compact form you can find where the gain appears as the leading term. I have built a quick Mathcad sheet showing the factorization steps in \$H_1\$, \$H_2\$ and \$H_3\$:
You have here a good source of information on the bandpass filters.