Median Bernoulli Numbers and Ramanujan’s Harmonic...
Leonhard Euler in 1755 applied the Euler–Maclaurin sum formula to find the famous standard Euler asymptotic expansion for 𝐻𝑛Hn as 𝑛→∞n→∞: 𝐻𝑛∼𝛾+log𝑛−∑𝑘=1∞𝐵𝑘𝑘·𝑛𝑘,Hn∼γ+logn−∑k=1∞Bkk·nk, (1) where 𝐵𝑘Bk is the Bernoulli num...