A269893 -id:A269893 - 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)).

A269892 Decimal expansion of the [negated] location of the maximum of the Airy function Ai.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Mar 07 2016

			-1.01879297164747108901732478339974382421820544125443456387...

L. D. Landau & E. M. Lifshitz, The Classical Theory of Fields, Pergamon Press 1971, page 150.

Eric Weisstein's MathWorld, Airy Functions

Cf. A269893 (value of maximum).

FindRoot[AiryAiPrime[x] == 0, {x, -1}, WorkingPrecision -> 103][[1, 2]] // 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)); -(left+right)/2; \\ Charles R Greathouse IV, Apr 26 2019

A385253 Decimal expansion of the function AiryAi(x) at x=1.

Original entry on oeis.org

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

Offset: 0

Artur Jasinski, Jul 29 2025

Second derivative at x=1 has that same value.

			0.1352924163128814155241474235154663...

Cf. A014402, A176730, A284867, A284868, A269893.

AiryAi(1) ; evalf(%) ; # R. J. Mathar, Jul 31 2025

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

airy(1)[1] \\ Michel Marcus, Jul 29 2025

Equals AiryAi''(1).

cp's OEIS Frontend

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

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

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A269892 Decimal expansion of the [negated] location of the maximum of the Airy function Ai.

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A385253 Decimal expansion of the function AiryAi(x) at x=1.

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