# Intrinsic volumes of ellipsoids

@inproceedings{Gusakova2022IntrinsicVO, title={Intrinsic volumes of ellipsoids}, author={Anna Gusakova and E. Spodarev and Dmitry Zaporozhets}, year={2022} }

. We deduce explicit formulae for the intrinsic volumes of an ellipsoid in R d , d ≥ 2, in terms of elliptic integrals. Namely, for an ellipsoid E ⊂ R d with semiaxes a 1 , . . . , a d we show that for all k = 1 , . . . , d , where s k − 1 is the ( k − 1)-th elementary symmetric polynomial and κ k is the volume of the k -dimensional unit ball. Some examples of the intrinsic volumes V k with low and high k are given where our formulae look particularly simple. As an application we derive new…

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