A203143 -id:A203143 - cp's OEIS frontend

A203146 Decimal expansion of Gamma(7/8).

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

Offset: 1

N. J. A. Sloane, Dec 29 2011

			1.0896523574228969512523767551028929711478700677675651205137...

Index to sequences related to the Gamma function.

Cf. A010767, A068465, A203143, A231863.

RealDigits[Gamma[7/8], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)

gamma(7/8) \\ Charles R Greathouse IV, Mar 25 2014

A068465 = A231863 * A010767 * A203143 * this. - R. J. Mathar, Jan 15 2021

A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Aug 11 2014

			0.02300458786273601031799260214514696231866764147508832909638...

Steven R. Finch, Errata and Addenda to Mathematical Constants. p. 8.

Cf. A203142, A203143, A203144, A203146.

s = (Pi/(2*Sqrt[2]))*(Log[Gamma[1/8]*Gamma[3/8]/(Gamma[5/8]*Gamma[7/8])] - (EulerGamma + Log[2*Pi])); Join[{0}, RealDigits[s, 10, 99] // First]

(Pi/(2*sqrt(3)))*(log(Gamma(1/8)/Gamma(3/8)/(Gamma(5/8)/Gamma(7/8))) - (gamma + log(2*Pi))), where gamma is Euler's constant and Gamma(x) is the Euler Gamma function.

A203127 Decimal expansion of (3/8)! = Gamma(11/8).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 29 2011

			0.88891356915622534074242756406624469120777530125959687041567...

Index to sequences related to the Gamma function.

Cf. A011027, A203130, A203143, A203146, A231863.

RealDigits[Gamma[11/8], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)

gamma(11/8) \\ Charles R Greathouse IV, Mar 25 2014

Equals 3*A203143/8. - R. J. Mathar, Jan 15 2021
A203146 * this * A231863 * A011027 = A203130. - R. J. Mathar, Jan 15 2021
Equals Integral_{x=0..oo} exp(-x^(8/3)) dx. - Ilya Gutkovskiy, Apr 10 2024

A359533 Decimal expansion of Sum_{k>=0} (-1/64)^kbinomial(2k, k)^3(4k + 1)*H_k, where H_k is the k-th harmonic number (negated).

Original entry on oeis.org

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

Offset: 0

Stefano Spezia, Jan 04 2023

			0.276427204245986573092639825616889946783740795...

John M. Campbell, Applications of a class of transformations of complex sequences, arXiv:2212.13305 [math.NT], 2022. See p. 6.

Cf. A000796, A001008, A002805, A002897, A016639, A016813, A063448, A068465, A068466, A091925, A203142, A203143.

Cf. A359532.

First[RealDigits[N[(Gamma[1/8]Gamma[3/8]/(Gamma[1/4]Gamma[3/4]))^2/(6Sqrt[2]Pi)-4Log[2]/Pi,100]]]

Equals 4*log(2)/Pi - (Gamma(1/8)*Gamma(3/8)/(Gamma(1/4)*Gamma(3/4)))^2/(6*sqrt(2)*Pi).

Equals 4*log(2)/Pi - (Gamma(1/8)*Gamma(3/8))^2/(12*sqrt(2)*Pi^3).

cp's OEIS Frontend

A203146 Decimal expansion of Gamma(7/8).

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A242011 Decimal expansion of sum_{k>=0} (-1)^k*(log(4k+1)/(4k+1)+log(4k+3)/(4k+3)).

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A203127 Decimal expansion of (3/8)! = Gamma(11/8).

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A359533 Decimal expansion of Sum_{k>=0} (-1/64)^k*binomial(2*k, k)^3*(4*k + 1)*H_k, where H_k is the k-th harmonic number (negated).

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A359533 Decimal expansion of Sum_{k>=0} (-1/64)^kbinomial(2k, k)^3(4k + 1)*H_k, where H_k is the k-th harmonic number (negated).