A358559 - OEIS

%I #18 Jan 06 2024 17:53:26

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

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

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

%N Decimal expansion of Bi(0), where Bi is the Airy function of the second kind.

%D F. W. J. Olver, Asymptotics and Special Functions, Academic Press, ISBN 978-0-12-525856-2, 1974.

%H [DLMF] NIST Digital Library of Mathematical Functions, <a href="https://dlmf.nist.gov/9.2.E5">Eq. 9.2.5</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AiryFunctions.html">Airy Functions</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Airy_function">Airy Function</a>.

%F Bi(0) = A284867*A002194.

%F Bi(0) = A358564*3.

%F Bi(0) = 1/(3^(1/6)*A073006).

%F Bi(0) = A073005/(3^(1/6)*A186706).

%F Bi(0) = A073005/(3^(1/6)*2*A093602).

%F Bi(0) = 3^(1/3)*A073005/(2*A000796).

%F Bi(0) = A252799/(3^(1/6)*BarnesG[5/3]).

%F Bi(0) = 3^(1/4)/(2^(2/9) * Pi^(1/3) * AGM(2,(sqrt(2+sqrt(3))))^(1/3)), where AGM is the arithmetic-geometric mean.

%e 0.61492662744600073515092236909361355359472818864859650504087875301429651...

%t RealDigits[AiryBi[0], 10, 120][[1]] (* _Amiram Eldar_, Nov 28 2022 *)

%o (PARI) airy(0)[2]

%o (PARI) airy(0)[1]*sqrt(3)

%o (PARI) 3^(1/3)*gamma(1/3)/(2*Pi)

%o (SageMath) airy_bi(0).n(algorithm='scipy', prec=250)

%Y Cf. A284867 (Ai(0)), A284868 (Ai'(0)), this sequence (Bi(0)), A358561 (Bi'(0)), A358564(Gi(0)).

%K cons,nonn

%O 0,1

%A _Dumitru Damian_, Nov 22 2022