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Search: id:A060506
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| A060506 |
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Numerators of the asymptotic expansion of the Airy function Ai(x). |
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+0
3
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| 1, 5, 385, 85085, 37182145, 5391411025, 5849680962125, 1267709431363375, 2562040760785380875, 6653619855759634132375, 4318199286388002551911375, 1556514560957130010757145625, 7404339766473067461171741738125
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The series arises in the asymptotic expansion of the Airy function A(x) for large |x| as Ai(x)~pi^(-1/2)/2*x^(-1/4)*exp(-z)*sum((-1)^k*c(k)*z^(-k),k=0..infinity), where z=2/3*x^(3/2). a(k) is the numerator of the fully canceled c(k).
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings).
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
NIST's Digital Library of Mathematical Functions, Airy and Related Functions (Poincare-Type Expansions) by Frank W. J. Olver.
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FORMULA
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a(k)=numer(product((2*l+1), l=k..3*k-1)/216^k/k!)
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EXAMPLE
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a(2)=385 because for k=2, product((2*l+1),l=k..3*k-1)/216^k/k! = 3465/23328 = 385/2592, and we take the numerator of the fully canceled fraction.
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CROSSREFS
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Cf. A060507.
Sequence in context: A098038 A072172 A100474 this_sequence A057633 A006700 A079011
Adjacent sequences: A060503 A060504 A060505 this_sequence A060507 A060508 A060509
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Michael Praehofer (praehofer(AT)ma.tum.de), Mar 22 2001
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