A103647 -id:A103647 - cp's OEIS frontend

A238388 Decimal expansion of x^(1/3) * y^(2/3), where x is the constant in A103647 and y is the constant in A238387.

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

Offset: 0

Eric M. Schmidt, Feb 26 2014

Occurs in a formula concerning the error in various approximations of binomial distributions. See [Prohorov].

			0.31295644329257221613608878676292116801179369870970508298082007371...

Yu. V. Prohorov, Asymptotic behavior of the binomial distribution. 1961. Select. Transl. Math. Statist. and Probability, Vol. 1 pp. 87-95. Inst. Math. Statist. and Amer. Math. Soc., Providence, R.I.

Yu. V. Prohorov, Asymptotic behavior of the binomial distribution, Uspekhi Mat. Nauk, 8:3(55) (1953), 135-142 (in Russian). See lambda p. 136.

Cf. A103647, A238387.

x = sqrt(2/Pi)*exp(-1/2); y = (1 + 4*exp(-3/2))/(3*sqrt(2*Pi)); x^(1/3) * y^(2/3) \\ Michel Marcus, Feb 27 2014

A238387 Decimal expansion of (1 + 4e^(-3/2))/(3sqrt(2*Pi)).

Original entry on oeis.org

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

Offset: 0

Eric M. Schmidt, Feb 26 2014

Occurs in a formula estimating the error in approximating a binomial distribution with a normal distribution. See [Prohorov].

			0.25166883335507952210292348310539606239875418040734266550892142061...

Yu. V. Prohorov, Asymptotic behavior of the binomial distribution. 1961. Select. Transl. Math. Statist. and Probability, Vol. 1 pp. 87-95. Inst. Math. Statist. and Amer. Math. Soc., Providence, R.I.

G. C. Greubel, Table of n, a(n) for n = 0..2500 [a(2500) corrected by _Georg Fischer_, Jun 23 2020]
Yu. V. Prohorov, Asymptotic behavior of the binomial distribution, Uspekhi Mat. Nauk, 8:3(55) (1953), 135-142 (in Russian). See lambda2 in theorem 3 p. 137.

Cf. A103647, A238388.

RealDigits[N[(1 + 4*Exp[-3/2])/(3*Sqrt[2*Pi]), 1001]] (* G. C. Greubel, Jan 26 2016 *)

(1 + 4*exp(-3/2))/(3*sqrt(2*Pi)) \\ Michel Marcus, Feb 27 2014

cp's OEIS Frontend

A238388 Decimal expansion of x^(1/3) * y^(2/3), where x is the constant in A103647 and y is the constant in A238387.

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A238387 Decimal expansion of (1 + 4e^(-3/2))/(3sqrt(2*Pi)).

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cp's OEIS Frontend

A238388 Decimal expansion of x^(1/3) * y^(2/3), where x is the constant in A103647 and y is the constant in A238387.

Views

Author

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References

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PARI

A238387 Decimal expansion of (1 + 4*e^(-3/2))/(3*sqrt(2*Pi)).

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Mathematica

PARI

A238387 Decimal expansion of (1 + 4e^(-3/2))/(3sqrt(2*Pi)).