cp's OEIS Frontend

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.

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

Original entry on oeis.org

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

Views

Author

Dumitru Damian, Nov 22 2022

Keywords

Examples

			0.61492662744600073515092236909361355359472818864859650504087875301429651...

References

  • F. W. J. Olver, Asymptotics and Special Functions, Academic Press, ISBN 978-0-12-525856-2, 1974.
  • Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 56, page 559.

Links

Crossrefs

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

Programs

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

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.

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

Original entry on oeis.org

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

Views

Author

Dumitru Damian, Nov 22 2022

Keywords

Examples

			0.44828835735382635791482371039882839086622679921226206108280877837233075...

References

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

Links

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.
Showing 1-2 of 2 results.

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