This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358561 #18 Feb 16 2025 08:34:04 %S A358561 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, %T A358561 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, %U A358561 0,7,5,5,0,0,9,7,8,0,6,4,7,1,8,5,0,4 %N A358561 Decimal expansion of the derivative Bi'(0), where Bi is the Airy function of the second kind. %D A358561 F. W. J. Olver, Asymptotics and Special Functions, Academic Press, ISBN 978-0-12-525856-2, 1974. %H A358561 [DLMF] NIST Digital Library of Mathematical Functions, <a href="https://dlmf.nist.gov/9.2.E6">Eq. 9.2.6</a>. %H A358561 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AiryFunctions.html">Airy Functions</a>. %H A358561 Wikipedia, <a href="https://en.wikipedia.org/wiki/Airy_function">Airy Function</a>. %F A358561 Bi'(0) = A284868*A002194. %F A358561 Bi'(0) = 3*Gi'(0), where Gi' is the derivative of the inhomogeneous Airy function of the first kind. %F A358561 Bi'(0) = 3^(1/6)/A073005. %F A358561 Bi'(0) = A073006*3^(1/6)/A186706. %F A358561 Bi'(0) = A073006*3^(1/6)/2*A093602. %F A358561 Bi'(0) = 3^(2/3)*A073006/(2*A000796). %F A358561 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. %e A358561 0.44828835735382635791482371039882839086622679921226206108280877837233075... %t A358561 RealDigits[AiryBi'[0], 10, 120][[1]] (* _Amiram Eldar_, Nov 28 2022 *) %o A358561 (PARI) derivnum(x=0, airy(x)[2]) %o A358561 (SageMath) airy_bi_prime(0).n(algorithm='scipy', prec=250) %Y A358561 Cf. A284867 (Ai(0)), A284868 (Ai'(0)), A358559 (Bi(0)), this sequence (Bi'(0)), A358564 (Gi(0)). %K A358561 cons,nonn %O A358561 0,1 %A A358561 _Dumitru Damian_, Nov 22 2022