A lot of sources stop expanding the taylor approximation at the second order Hessian matrix for a multivariable function. I'd like to include the third order taylor expansion. Does anyone have the matrix equation for this and have any sources talking about it? Is there a name for the third order derivative matrix?
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1matrix equation? No. But, see my answers in General form third degree multi variable Taylor polynomial and more generally, Taylor Series coordinate free form. – peek-a-boo Jun 25 '23 at 01:37
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https://sites.math.washington.edu/~folland/Math425/taylor2.pdf – Andrew Jun 25 '23 at 01:37