The following first order asymptotics is well-known $P(\|W\|_\infty < r)=\exp\{-\frac{\pi^2}{8 r^2}(1+o(1))\}$ as $r\to 0$, where $W$ is the Wiener process on [0,1].

Does anybody meet an exact formula for $P(\|W\|_\infty < r)=?$ (for arbitrary $0<r<1$) or at least more precise asymptotics (the second or the third order)?

The following first order asymptotics is well-known: $P(\|W\|_\infty < r)=\exp\{-\frac{\pi^2}{8 r^2}(1+o(1))\}$ as $r\to 0$, where $W$ is the Wiener process on [0,1].

Has anybody met an exact formula for $P(\|W\|_\infty < r)=?$ (for arbitrary $0<r<1$) or at least more precise asymptotics (the second or the third order)?

The following first order asymptotics is well-known $P(||W||_{\infty}< r)=\exp\{-\frac{\pi^2}{8 r^2}(1+o(1))\}$ as $r\to 0$, where $W$ is the Wiener process on [0,1].

Does anybody meet an exact formula for $P(||W||_{\infty}< r)=?$ (for arbitrary $0<r<1$) or at least more precise asymptotics (the second or the third order)?

The following first order asymptotics is well-known $P(\|W\|_\infty < r)=\exp\{-\frac{\pi^2}{8 r^2}(1+o(1))\}$ as $r\to 0$, where $W$ is the Wiener process on [0,1].

Does anybody meet an exact formula for $P(\|W\|_\infty < r)=?$ (for arbitrary $0<r<1$) or at least more precise asymptotics (the second or the third order)?