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.

Showing 1-3 of 3 results.

A284867 Decimal expansion of Ai(0), where Ai is the Airy function of the first kind.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 04 2017

Keywords

Examples

			0.35502805388781723926006318600418317639797917419917724058332651030081...

References

  • Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 56, page 559.

Links

Crossrefs

Cf. A096714, A096715, A269892, A269893, A073006 (Gamma(2/3)), A284868 (Ai'(0)).

Programs

Formula

Ai(0) = 1/(3^(2/3)*Gamma(2/3)).

A284868 Decimal expansion of the derivative Ai'(0) (negated), where Ai is the Airy function of the first kind.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Apr 04 2017

Keywords

Examples

			-0.2588194037928067984051835601892039634790911383549345822100018138561...

Links

Crossrefs

Cf. A096714, A096715, A269892, A269893, A073005 (Gamma(1/3)), A284867 (Ai(0)).

Programs

  • Mathematica
    RealDigits[AiryAi'[0], 10, 105][[1]]
  • PARI
    -derivnum(x=0,airy(x)[1]) \\ Charles R Greathouse IV, Apr 26 2019

Formula

Ai'(0) = -1/(3^(1/3)*Gamma(1/3)).

A096714 First (least negative) real zero of the Airy Ai function (negated).

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Jul 04 2004

Keywords

Examples

			-2.33810741045976703848919725244673544063854014567238...

Links

Crossrefs

Cf. A096715.

Programs

  • Mathematica
    RealDigits[AiryAiZero[1], 10, 100][[1]] (* Amiram Eldar, Jun 27 2021 *)
  • PARI
    Ain(x)=sqrt((-x)/9)*(besselj(1/3,2/3*(-x)^(3/2)) + besselj(-1/3,2/3*(-x)^(3/2))) \\ Airy function Ai(x) for x < 0
-solve(x=-2.5,-2.2,Ain(x)) \\ Thomas König, Jan 29 2017
  • PARI
    -solve(x=-2.4,-2.3, airy(x)[1]) \\ Charles R Greathouse IV, Apr 27 2019
  • PARI
    solve(s=1,2, t=2/3*s^3; (besselj(1/3, t) + besselj(-1/3, t))*s)^2 \\ Charles R Greathouse IV, Aug 09 2022
Showing 1-3 of 3 results.

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