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Related to Steiner Formula (which gives a polynomial expansion of Volume after Minkowski Sum of a Convex Body and Ball with some radius $r$):

I want to know what would be $quermassintegral$ of an Interval and a Unit Ball (all $quermassintegral$'s, i.e.: from first to n-th.)

Note: I am not sure if $quermassintegral$ is the correct name, but what I mean are terms in the expansion, other than powers of the radius and binomial coefficients.

I have already checked couple books now, but neither are explicitly providing a way to find out an answer for my question. Text/Book advice would be appreciated as well.

Ekber
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  • You answered your own question with the same book reference twice. https://math.stackexchange.com/questions/2665385/mean-width-and-diamk/2749238#2749238 . Please stop this nonsense. – Jack D'Aurizio Apr 23 '18 at 16:26
  • This is not a nonsense, please check the book. The book explains both the relation between the mean-width and diameter of a Convex Hull, and give precise statement and explanation for Steiner's Formula. Quermassintegrals and Mixed Volumes are defined as well in the meantime. – Ekber Apr 23 '18 at 21:24
  • The book is nice, indeed, buy you answering your own questions twice with the same book recommendation is nonsense. – Jack D'Aurizio Apr 23 '18 at 21:41

1 Answers1

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Hug, Daniel; Weil, Wolfgang, $\textit{A Course on Convex Geometry}$. Very nice book if you are interested in Convex Geometry; explains the above mentioned property.

Ekber
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