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coefficient calculations

1.where can i finde the transfer function and coefficients? 1st-Order Low-Pass / High-Pass,Peaking,Notch,Chebyshev Low-Pass / High-Pass.

2.I know the contents of this conversion formula, such as what does S mean?

https://wiki.analog.com/resources/tools-software/sigmastudio/toolbox/filters/general2ndorder