Simple algebra clarification needed for Gaussian entropy formula Norwich (2003) gives

Gwendolyn Giles

Gwendolyn Giles

Answered question

2022-01-22

Simple algebra clarification needed for Gaussian entropy formula
Norwich (2003) gives the following equality based on a substitution
H=12ln(2πσ2)+12

Answer & Explanation

Amina Hall

Amina Hall

Beginner2022-01-23Added 11 answers

We have
12ln(2πσ2)+12=12ln(2πσ2)+12lne
12(ln(2πσ2)+lne)
=12ln(2πeσ2)
It is the +12 on the right side that gets an extra factor of lne. Then we use distribution, and finally elementary logarithm rules to put the two logarithms together into one.

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