A358559 Decimal expansion of Bi(0), where Bi is the Airy function of the second kind.

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

Offset

0,1

References

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

Links

Table of n, a(n) for n=0..84.

[DLMF] NIST Digital Library of Mathematical Functions, Eq. 9.2.5.

Eric Weisstein's World of Mathematics, Airy Functions.

Wikipedia, Airy Function.

Formula

Bi(0) = A284867*A002194.

Bi(0) = A358564*3.

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

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

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

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

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

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.

Example

0.61492662744600073515092236909361355359472818864859650504087875301429651...

Mathematica

RealDigits[AiryBi[0], 10, 120][[1]] (* Amiram Eldar, Nov 28 2022 *)

Prog

(PARI) airy(0)[2]
(PARI) airy(0)[1]*sqrt(3)
(PARI) 3^(1/3)*gamma(1/3)/(2*Pi)
(SageMath) airy_bi(0).n(algorithm='scipy', prec=250)

Crossrefs

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

Sequence in context: A068226 A011237 A195433 * A367563 A016534 A230821

Adjacent sequences: A358556 A358557 A358558 * A358560 A358561 A358562

Keyword

cons,nonn

Author

Dumitru Damian, Nov 22 2022

Status

approved