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removed capitals from title (the question was bumped anyway)
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YCor
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The Hubbard-Stratonovich Transformationtransformation

is there a way to extend the Hubbard-Stratonovich Transformationtransformation $$e^{\frac{1}{2}Ks^2}=\left(\frac{K}{2\pi}\right)^{1/2}\int_{–\infty}^\infty e^{–Kx^2+Ksx}dx$$ to the case $e^{\frac{1}{2}Ks^p}$ for $p \in \mathbb{N}$?

The Hubbard-Stratonovich Transformation

is there a way to extend the Hubbard-Stratonovich Transformation $$e^{\frac{1}{2}Ks^2}=\left(\frac{K}{2\pi}\right)^{1/2}\int_{–\infty}^\infty e^{–Kx^2+Ksx}dx$$ to the case $e^{\frac{1}{2}Ks^p}$ for $p \in \mathbb{N}$?

The Hubbard-Stratonovich transformation

is there a way to extend the Hubbard-Stratonovich transformation $$e^{\frac{1}{2}Ks^2}=\left(\frac{K}{2\pi}\right)^{1/2}\int_{–\infty}^\infty e^{–Kx^2+Ksx}dx$$ to the case $e^{\frac{1}{2}Ks^p}$ for $p \in \mathbb{N}$?

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HyyFly
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The Hubbard-Stratonovich Transformation

is there a way to extend the Hubbard-Stratonovich Transformation $$e^{\frac{1}{2}Ks^2}=\left(\frac{K}{2\pi}\right)^{1/2}\int_{–\infty}^\infty e^{–Kx^2+Ksx}dx$$ to the case $e^{\frac{1}{2}Ks^p}$ for $p \in \mathbb{N}$?