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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 4th 2013
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeAug 28th 2018

started a note on worldsheet and brane instantons (here) but not optimized for public consumption yet

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeOct 19th 2020

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeAug 23rd 2021

Strictly speaking, the $n$-th derivatives for the function $g \mapsto e^{-1/g^2}$ don’t exist at $g = 0$, because $g \mapsto -1/g^2$ and thus $g \mapsto e^{-1/g^2}$ is only defined for $g \gt 0$ or $g \lt 0$. One could analytically continue $g \mapsto e^{-1/g^2}$ and its $n$-th derivatives to $g = 0$ via a piecewise function
$g \mapsto \begin{cases} e^{-1/g^2} & g \gt 0 \vee g \lt 0 \\ 0 & g = 0 \end{cases}$
and similarly for its $n$-th derivatives, but in that case, it shouldn’t be surprised that this function’s taylor series expansion at zero is only valid at zero. It’s the same reason why the taylor series expansion for the absolute value function as the identity function on the real numbers is only valid for the positive real numbers, and is inherently due to the piecewise nature of the function.