Euclidean oscillator diagonal kernel
= Euclidean oscillator diagonal kernel
{c}
At imaginary duration $\beta\hbar$, $K_E(q,q)=\sqrt{m\omega/[2\pi\hbar\sinh x]}\exp[-m\omega q^2\tanh(x/2)/\hbar]$, $x=\beta\hbar\omega$. Integrating the common endpoint yields $[2\sinh(x/2)]^{-1}$.