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
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
KEYWORD
cons,nonn
AUTHOR
Dumitru Damian, Nov 22 2022
STATUS
approved