A203130 -id:A203130 - cp's OEIS frontend

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

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

A256930 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)(3/4)^(2*k).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Apr 13 2015

			1.2036214036775919014128244060883195641815351691976781420672...

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights, 2011, p. 272, eq. (31).

Eric Weisstein's MathWorld, Riemann Zeta Function.
Wikipedia, Riemann zeta function.

Cf. A068466, A203130, A256929.

RealDigits[Log[3*Pi/(2*Sqrt[2])], 10, 107] // First

log(3*Pi/(2*sqrt(2))) \\ Michel Marcus, Apr 13 2015

Equals log(Gamma(1/4)*Gamma(7/4)).

Equals log(3*Pi/(2*sqrt(2))).

Name corrected by Amiram Eldar, Oct 12 2024

A257094 Decimal expansion of Gamma(9/4).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Apr 16 2015

			1.13300309631934634747833911120864750093598990090002...

Eric Weisstein's MathWorld, Gamma Function.
Wikipedia, Particular values of the Gamma function.

Cf. A068466 (Gamma(1/4)), A068465 (3/4), A068467 (5/4), A203130 (7/4), A257095 (11/4).

RealDigits[Gamma[9/4], 10, 102] // First

gamma(9/4) \\ Michel Marcus, Apr 16 2015

Equals (5/16)*Gamma(1/4).

A257095 Decimal expansion of Gamma(11/4).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Apr 16 2015

			1.6083594219855456592319415231637938164922515131418426772395311...

David H. Bailey and Simon Plouffe, Recognizing Numerical Constants, (1995).
Eric Weisstein's MathWorld, Gamma Function
Wikipedia, Particular values of the Gamma function

Cf. A068466 (Gamma(1/4)), A068465 (3/4), A068467 (5/4), A203130 (7/4), A257094 (9/4).

RealDigits[Gamma[11/4], 10, 104] // First

gamma(11/4) \\ Michel Marcus, Apr 16 2015

(21/16)*Pi*sqrt(2)/Gamma(1/4).

Also equals Integral_{0..infinity} t^(7/4)*exp(-t) dt.

A203132 Decimal expansion of (7/8)! = Gamma(15/8).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Dec 29 2011

			0.95344581274503483234582966071503134975438630929661948044949...

Index to sequences related to the Gamma function

RealDigits[(7/8)!,10,120][[1]] (* Harvey P. Dale, Jun 23 2016 *)

gamma(15/8) \\ Charles R Greathouse IV, Mar 25 2014

Equals 7*A203146/8. - R. J. Mathar, Jan 15 2021
A203127 * this * A231863*2^(9/4) = (7/4)* A203130. - R. J. Mathar, Jan 15 2021
Equals Integral_{x=0..oo} exp(-x^(8/7)) dx. - Ilya Gutkovskiy, Apr 10 2024

cp's OEIS Frontend

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

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A256930 Decimal expansion of Sum_{k>=1} (zeta(2*k)/k)*(3/4)^(2*k).

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A257094 Decimal expansion of Gamma(9/4).

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A257095 Decimal expansion of Gamma(11/4).

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A203132 Decimal expansion of (7/8)! = Gamma(15/8).

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A256930 Decimal expansion of Sum_{k>=1} (zeta(2k)/k)(3/4)^(2*k).