grandes-ecoles 2022 Q16

grandes-ecoles · France · mines-ponts-maths1__psi Taylor series Taylor's formula with integral remainder or asymptotic expansion

Conclude that $$\ln P(e^{-t}) = \frac{\pi^2}{6t} + \frac{\ln(t)}{2} - \frac{\ln(2\pi)}{2} + o(1) \text{ when } t \text{ tends to } 0^+.$$

Conclude that
$$\ln P(e^{-t}) = \frac{\pi^2}{6t} + \frac{\ln(t)}{2} - \frac{\ln(2\pi)}{2} + o(1) \text{ when } t \text{ tends to } 0^+.$$