0881132人目の素数さん
2018/11/18(日) 02:23:36.94ID:ENzLbcNDlog {(m+n+1)!} > (m+n+3/2) log(m+n) - (m+n) + 0.8918
(略証)
log(k) > ∫[k-1/2,k+1/2] log(x)dx より
log{(m+n+1)!} = Σ[k=2,m+n+1] log(k)
> ∫[3/2,m+n+3/2] log(x)dx
= [ x・log(x) -x ](x=3/2,m+n+3/2)
= (m+n+3/2) log(m+n+3/2) -(m+n) -(3/2)log(3/2)
> (m+n+3/2) log(m+n) +(3/2) - (m+n) - (3/2)log(3/2)
= (m+n+3/2) log(m+n) - (m+n) + 0.8918023378