A245532 - OEIS

%I #24 Feb 24 2023 04:41:30

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

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

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

%N Decimal expansion of b_3, a constant associated with the 3rd Du Bois Reymond constant.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.12 Du Bois Reymond Constants, pp. 238-239.

%H Vincenzo Librandi, <a href="/A245532/b245532.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/duBois-ReymondConstants.html">du Bois-Reymond Constants</a>.

%F b_3 = (-1/4)*(e^3 - 3*e - 12).

%F Equals 2*sum((-1)^(n+1)/(1+xi(n)^2)^(3/2), (n=1..infinity)), where xi(n) is the n-th positive solution to tan(x)=x.

%e 0.017327140547366991288083189869067399070958360636432145130492163368346...

%p Digits:=100: evalf((-1/4)*(exp(3)-3*exp(1)-12)); # _Wesley Ivan Hurt_, Jul 26 2014

%t b3 = (-1/4)*(E^3 - 3*E - 12); Join[{0}, RealDigits[b3, 10, 101] // First]

%o (PARI) (12+3*exp(1)-exp(3))/4 \\ _Charles R Greathouse IV_, Jul 25 2014

%Y Cf. A224196.

%K nonn,cons,easy

%O 0,3

%A _Jean-François Alcover_, Jul 25 2014