Frequency modulator sensitivity and Quadrature demod gain

[Fernando]

In the GRC Frequency mod block  the doc says


analog_frequency_modulator_fc
make(float sensitivity) -> frequency_modulator_fc_sptr
        Frequency modulator block.
        float input; complex baseband output
        Takes a real, baseband signal (x_m[n]) and output a frequency 
modulated signal (y[n]) according to:

        Where x[n] is the input sample at time n and  is the frequency 
deviation. Common values for  are 5 kHz for narrowband FM channels such 
as for voice systems and 75 KHz for wideband FM, like audio broadcast FM 
stations.
        In this block, the input argument is , not the frequency 
deviation. The sensitivity specifies how much the phase changes based on 
the new input sample. Given a maximum deviation, , and sample rate , the 
sensitivity is defined as:
        Constructor Specific Documentation:
        Build a frequency modulator block.
        Args:
            sensitivity : radians/sample = amplitude * sensitivity


There is somejhing missing at:   " Where x[n] is the input sample at 
time n and  ____________  is the frequency deviation"


Here https://wiki.gnuradio.org/index.php/Frequency_Mod the same is 
missing too.

I guess it refers to  sensitivity = K = 
(2*pi*freq_deviation)/samp_rate    correct?


Second question related to this one.

If I the use Quadrature_demod for demodulation of the signal, the gain 
parameter will be the inverso of this one isnt it?


gain=samp_rate/((2*pi*freq_deviation)   but when I insert the quadrature 
demod block it is autofilled with

samp_rate/(2*math.pi*fsk_deviation_hz/8.0)   where does the 8.0 come from?



best regards