A358561 Decimal expansion of the derivative Bi'(0), where Bi is the Airy function of the second kind.

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

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..85.

[DLMF] NIST Digital Library of Mathematical Functions, Eq. 9.2.6.

Eric Weisstein's World of Mathematics, Airy Functions.

Wikipedia, Airy Function.

Formula

Bi'(0) = A284868*A002194.

Bi'(0) = 3*Gi'(0), where Gi' is the derivative of the inhomogeneous Airy function of the first kind.

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

Bi'(0) = A073006*3^(1/6)/A186706.

Bi'(0) = A073006*3^(1/6)/2*A093602.

Bi'(0) = 3^(2/3)*A073006/(2*A000796).

Bi'(0) = 3^(1/4)*AGM(2,(sqrt(2+sqrt(3))))^(1/3)/(2^(7/9) * Pi^(2/3)), where AGM is the arithmetic-geometric mean.

Example

0.44828835735382635791482371039882839086622679921226206108280877837233075...

Mathematica

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

Prog

(PARI) derivnum(x=0, airy(x)[2])
(SageMath) airy_bi_prime(0).n(algorithm='scipy', prec=250)

Crossrefs

Cf. A284867 (Ai(0)), A284868 (Ai'(0)), A358559 (Bi(0)), this sequence (Bi'(0)), A358564 (Gi(0)).

Sequence in context: A181387 A091671 A137797 * A176295 A140874 A355234

Adjacent sequences: A358558 A358559 A358560 * A358562 A358563 A358564

Keyword

cons,nonn

Author

Dumitru Damian, Nov 22 2022

Status

approved