A068467 -id:A068467 - cp's OEIS frontend

A257095 Decimal expansion of Gamma(11/4).

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.

A371855 Decimal expansion of Integral_{x=-oo..oo} exp(-x^4) dx.

Original entry on oeis.org

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

Offset: 1

Ilya Gutkovskiy, Apr 09 2024

			1.8128049541109541559653425779338360014975838...

Cf. A002161, A068466, A068467.

Mathematica
```
RealDigits[2 Gamma[5/4], 10, 104][[1]]
```

Equals 2 * Gamma(5/4).
Equals 2 * A068467.
Equals A068466 / 2.

A371856 Decimal expansion of Integral_{x=0..oo} exp(-x^5) dx.

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Apr 09 2024

			0.91816874239976061064095165518583040068682...

Index to sequences related to the Gamma function

Decimal expansion of Integral_{x=0..oo} exp(-x^k) dx: A019704 (k=2), A202623 (k=3), A068467 (k=4), this sequence (k=5), A203126 (k=6), A371857 (k=7), A203125 (k=8).

Cf. A175380.

Mathematica
```
RealDigits[Gamma[6/5], 10, 104][[1]]
```

Equals Gamma(6/5).

Equals A175380 / 5.

A371857 Decimal expansion of Integral_{x=0..oo} exp(-x^7) dx.

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Apr 09 2024

			0.9354375628925463482448704784898566089...

Index to sequences related to the Gamma function

Decimal expansion of Integral_{x=0..oo} exp(-x^k) dx: A019704 (k=2), A202623 (k=3), A068467 (k=4), A371856 (k=5), A203126 (k=6), this sequence (k=7), A203125 (k=8).

Cf. A220086.

Mathematica
```
RealDigits[Gamma[8/7], 10, 106][[1]]
```

Equals Gamma(8/7).

Equals A220086 / 7.

A068151 Continued fraction for Gamma(5/4).

Original entry on oeis.org

0, 1, 9, 1, 2, 6, 16, 2, 2, 1, 1, 1, 1, 1, 1, 4, 2, 1, 2, 1, 1, 1, 4, 2, 1, 1, 2, 1, 1, 2, 1, 20, 1, 1, 4, 34, 3, 1, 18, 1, 1, 27, 1, 4, 1, 58, 1, 2, 5, 1, 4, 1, 24, 1, 1, 1, 1, 1, 3, 9, 3, 1, 1, 1, 6, 1, 1, 1, 52, 24, 4, 1, 16, 1, 1, 1, 1, 4, 1, 3, 1, 3, 3, 1, 1, 3, 2, 4, 3, 1

Offset: 0

Benoit Cloitre, Mar 13 2002

Cf. A068467 (decimal expansion).

Offset changed by Andrew Howroyd, Jul 06 2024

A071003 Binary expansion of Gamma(5/4).

Original entry on oeis.org

1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1

Offset: 0

Benoit Cloitre, May 18 2002

The same sequence of digits as A071002, because Gamma(5/4) = (1/4)*Gamma(1/4). - R. J. Mathar, Feb 21 2009

			0.1110100...

Cf. A068467, A071002.

RealDigits[Gamma[5/4], 2, 100][[1]] (* Amiram Eldar, May 04 2022 *)

Offset corrected by R. J. Mathar, Feb 05 2009

A377542 Decimal expansion of Gamma(1/4)^4/(16*Pi^2).

Original entry on oeis.org

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

Offset: 1

Stefano Spezia, Oct 31 2024

			1.09421980761323831941838497035223227162968636141...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 134.
Index to sequences related to the Gamma function.
Index entries for transcendental numbers.

Cf. A002388, A068465, A068466, A068467, A254794.

RealDigits[Gamma[1/4]^4/(16Pi^2),10,100][[1]]

Equals Product_{n>=1} (1 - 1/(2*n + 1)^2)^(-1)^n (see Finch).
Equals Product_{n>=1} (4*n - 1)^2*((4*n + 1)^2 - 1)/(((4*n - 1)^2 - 1)*(4*n + 1)^2) (see Shamos).
Equals 2*(Gamma(5/4)/Gamma(3/4))^2.
Equals A254794/2. - Hugo Pfoertner, Oct 31 2024

cp's OEIS Frontend

A257095 Decimal expansion of Gamma(11/4).

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A371855 Decimal expansion of Integral_{x=-oo..oo} exp(-x^4) dx.

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A371856 Decimal expansion of Integral_{x=0..oo} exp(-x^5) dx.

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A371857 Decimal expansion of Integral_{x=0..oo} exp(-x^7) dx.

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A068151 Continued fraction for Gamma(5/4).

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A071003 Binary expansion of Gamma(5/4).

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A377542 Decimal expansion of Gamma(1/4)^4/(16*Pi^2).

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