A253300 - OEIS

%I #12 May 22 2024 11:26:08

%S 6,5,8,5,8,2,3,5,4,1,0,9,0,9,3,5,6,5,4,6,9,6,5,6,8,5,3,4,0,3,6,4,4,1,

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

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

%N Decimal expansion of integral_{x=0..1} x^sqrt(x) dx.

%D Paul J. Nahin, Inside Interesting Integrals, Springer 2014, ISBN 978-1493912766.

%H Paul J. Nahin, <a href="https://doi.org/10.1007/978-3-030-43788-6">Inside interesting integrals</a>, Undergrad. Lecture Notes in Physics, Springer (2020), (6.1.6)

%F Equals sum_{n >= 1} (-1)^(n + 1)*(2/(n + 1))^n.

%e 0.6585823541090935654696568534036441701564...

%t NIntegrate[x^Sqrt[x], {x, 0, 1}, WorkingPrecision -> 110] // RealDigits[#, 10, 105]& // First

%o (PARI) intnum(x=0,1, x^sqrt(x)) \\ _Michel Marcus_, Dec 30 2014

%Y Cf. A073009, A083648, A253299.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Dec 30 2014