A373862 Decimal expansion of Sum_{k >= 1} log(k)/(k*sqrt(k+1)).

3, 7, 7, 1, 0, 0, 9, 4, 9, 1, 4, 0, 0, 9, 2, 3, 2, 2, 6, 0, 7, 9, 0, 8, 1, 1, 3, 7, 6, 7, 7, 3, 3, 8, 4, 1, 2, 4, 3, 5, 0, 9, 3, 6, 9, 9, 8, 4, 2, 2, 3, 1, 9, 0, 7, 3, 0, 0, 0, 9, 4, 4, 5, 9, 5, 9, 1, 8, 9, 2, 3, 5, 5, 0, 5, 6, 2, 1, 7, 4, 2, 9, 2, 2, 9, 0, 5, 2, 2, 9, 5, 7, 1, 7, 9, 9, 3, 6, 0, 5, 6, 7, 4, 6, 3

Offset: 1

Author

R. J. Mathar, Jun 19 2024

Keywords

• nonn
• cons

Examples

			3.77100949140092...
		

Links

• Math StackExchange, How do I test for convergence of log(n)/n/sqrt(n+1), (2019)

Crossrefs

Cf. A131688.

Programs

Maple

Digits := 120 ;
x := 0.0 ;
for l from 0 to 600 do
    x := x+(-1)^(l+1)*doublefactorial(2*l-1)/doublefactorial(2*l)*Zeta(1,3/2+l) ;
    x := evalf(x) ;
    print(x) ;
end do: # R. J. Mathar, Jun 27 2024

PARI

default(realprecision, 200); sumalt(k=0, (-1)^(k+1) * (2*k)! * zeta'(k+3/2) / (k!^2 * 4^k)) \\ Vaclav Kotesovec, Jun 27 2024

Formula

Equals sum_{l>=0} (-1)^(l+1) (2l-1)!! *Zeta'(3/2+l) /(2l)!!.

Extensions

More terms from Vaclav Kotesovec, Jun 27 2024