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A358564
Decimal expansion of Gi(0), where Gi is the inhomogeneous Airy function of the first kind (also called Scorer function).
2
2, 0, 4, 9, 7, 5, 5, 4, 2, 4, 8, 2, 0, 0, 0, 2, 4, 5, 0, 5, 0, 3, 0, 7, 4, 5, 6, 3, 6, 4, 5, 3, 7, 8, 5, 1, 1, 9, 8, 2, 4, 2, 7, 2, 9, 5, 4, 9, 5, 3, 2, 1, 6, 8, 3, 4, 6, 9, 5, 9, 5, 8, 4, 3, 3, 8, 0, 9, 8, 8, 3, 9, 7, 6, 8, 5, 0, 6, 8, 8, 0, 1, 7, 6, 4, 6, 2
OFFSET
0,1
REFERENCES
Scorer, R. S., Numerical evaluation of integrals of the form Integral_{x=x1..x2} f(x)*e^(i*phi(x))dx and the tabulation of the function Gi(z)=(1/Pi)*Integral_{u=0..oo} sin(u*z+u^3/3) du, Quart. J. Mech. Appl. Math. 3 (1950), 107-112.
LINKS
Amparo Gil, Javier Segura, and Nico Temme, On nonoscillating integrals for computing inhomogeneous Airy functions, Mathematics of Computation 70.235 (2001): 1183-1194.
[DLMF] NIST Digital Library of Mathematical Functions, Eq. 9.12.6.
Allan J. MacLeod, Computation of inhomogeneous Airy functions, Journal of Computational and Applied Mathematics, Volume 53, Issue 1, 1994, Pages 109-116, ISSN 0377-0427.
Wikipedia, Scorer Function.
FORMULA
Gi(0) = A358559/3.
Gi(0) = A284867/A002194.
Gi(0) = Hi(0)/2, where Hi is the inhomogeneous Airy function of the second kind.
Gi(0) = 1/(3^(7/6)*A073006).
Gi(0) = A073005/(3^(7/6)*A186706).
Gi(0) = A073005/(3^(7/6)*2*A093602).
Gi(0) = A073005/(3^(4/6)*2*A000796).
Gi(0) = A252799/(3^(7/6)*BarnesG(5/3)).
Gi(0) = 1/(3^(3/4) * 2^(2/9) * Pi^(1/3) * AGM(2,(sqrt(2+sqrt(3))))^(1/3)), where AGM is the arithmetic-geometric mean.
EXAMPLE
0.204975542482000245050307456364537851198242729549532168346959584338098839...
MATHEMATICA
First[RealDigits[N[ScorerGi[0], 90]]] (* Stefano Spezia, Nov 28 2022 *)
PROG
(PARI) airy(0)[2]/3
(PARI) 1/(3^(7/6)*gamma(2/3))
(PARI) sqrt(3)*gamma(1/3)/(3^(7/6)*2*Pi)
(PARI) 1/(3^(3/4)*2^(2/9)*Pi^(1/3)*sqrtn(agm(2, (sqrt(2+sqrt(3)))), 3))
(SageMath) 1/(3^(7/6)*gamma(2/3)).n(algorithm='scipy', prec=250)
CROSSREFS
Cf. A284867 (Ai(0)), A284868 (Ai'(0)), A358559 (Bi(0)), A358561 (Bi'(0)), this sequence (Gi(0)).
Sequence in context: A021492 A342201 A287314 * A077119 A002938 A111938
KEYWORD
cons,nonn
AUTHOR
Dumitru Damian, Nov 22 2022
STATUS
approved