There is conflict in caculating "Q" in shelving iir_filter, from parameter to coefficient. Which one is correct?

Quetion1:

In the literature "Cookbook formulae for audio EQ biquad filter coefficients" by Robert Bristow-Johnson, "Q" can be gotten by the equation as follows:

1/Q = sqrt((A + 1/A)*(1/S - 1) + 2) (1)

Here "*"is used.

In the contrast, in another literature " 1st-2nd-Order_IIR_Coefficient_Calculator", Which the link site is given by Mr. kJBob. The equation is like this:

1/Q=(SQRT((K11+1/K11)^(1/K7-1)+2) /k11=A, k7=S. (2)
Here , the algorithm "*" is taken place by "^". The "multiplication" changes to "exponential". The difference is too large.

Than, which one is correct!

Quetion 2: about "Q"and"S" in the shelving iir moudle filter .

In the sigmastudio GUI_DEV based on 1701 chip, we can module the shelving filter directly from the four parameters : f0/fs, Q, boost, and gain.
First, Whether the definition "Q" here is the same definition as the parameter in the equation (1).

Second, since we have the "Q" parameter before "S (shelf slop) in the adau1701", and "S" is something difficult to understand and get directly from the filter figure.
Is it correct and necessary to derive S from Q from the equation (2)?
S= f(A, Q) (3)

Equation(3)means a function derived from (2). And S is a parameter about A , and Q. Isn't it correct?

Thanks a lot!