A269892 -id:A269892 - cp's OEIS frontend

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

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

Jean-François Alcover, Apr 04 2017

			0.35502805388781723926006318600418317639797917419917724058332651030081...

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

Simon Plouffe, Airy Functions Constant C1.
Eric Weisstein's MathWorld, Airy Functions.
Wikipedia, Airy Function.

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

Mathematica
```
RealDigits[AiryAi[0], 10, 105][[1]]
```

airy(0)[1] \\ Charles R Greathouse IV, Apr 26 2019

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

Jean-François Alcover, Apr 04 2017

			-0.2588194037928067984051835601892039634790911383549345822100018138561...

Simon Plouffe, Airy Functions Constant C2
Eric Weisstein's MathWorld, Airy Functions
Wikipedia, Airy Function

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

Mathematica
```
RealDigits[AiryAi'[0], 10, 105][[1]]
```

-derivnum(x=0,airy(x)[1]) \\ Charles R Greathouse IV, Apr 26 2019

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

A269893 Decimal expansion of the value of the maximum of the Airy function Ai.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Mar 07 2016

			0.53565665601569986114486020069532285486973173723298325936484...

Eric Weisstein's MathWorld, Airy Functions

Cf. A269892 (location of maximum).

FindRoot[AiryAiPrime[x] == 0, {x, -1}, WorkingPrecision -> 104][[1, 2]] // AiryAi // RealDigits // First

computeAtCurrentPrecision()=my(left=-2., right=-1., e=4.>>bitprecision(1.)); while(right-left>e, my(L=(2*left+right)/3, R=(left+2*right)/3); if(airy(L)[1] < airy(R)[1], left=L, right=R)); airy((left+right)/2)[1]; \\ Charles R Greathouse IV, Apr 26 2019

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A269893 Decimal expansion of the value of the maximum of the Airy function Ai.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI