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

Author

Dumitru Damian, Nov 22 2022

Keywords

• cons
• nonn

Examples

			0.44828835735382635791482371039882839086622679921226206108280877837233075...
		

References

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

Links

• [DLMF] NIST Digital Library of Mathematical Functions, Eq. 9.2.6.
• Eric Weisstein's World of Mathematics, Airy Functions.
• Wikipedia, Airy Function.

Crossrefs

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

Programs

Mathematica

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

PARI

derivnum(x=0, airy(x)[2])

SageMath

airy_bi_prime(0).n(algorithm='scipy', prec=250)

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.