cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A371824 Decimal expansion of Pi^(1/2)*Gamma(1/10)/(5*Gamma(3/5)).

Original entry on oeis.org

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

Views

Author

Takayuki Tatekawa, Apr 07 2024

Keywords

Comments

Constants from generalized Pi integrals: the case of n=10.

Examples

			2.264617395043150744291188990313...

Links

Crossrefs

Cf. A085565, A113477, A262427.

Programs

  • Mathematica
    RealDigits[2*Sqrt[Pi]/10*Gamma[1/10]/Gamma[3/5], 10, 5001][[1]]
RealDigits[GoldenRatio * Gamma[1/5] * Gamma[2/5]^2 / (2^(6/5) * Sqrt[5] * Pi), 10, 120][[1]] (* Vaclav Kotesovec, Apr 07 2024 *)

Formula

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^10).
Equals phi * Gamma(1/5) * Gamma(2/5)^2 / (2^(6/5) * sqrt(5) * Pi), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Apr 07 2024

A371930 Decimal expansion of Pi^(1/2)*Gamma(1/14)/(7*Gamma(4/7)).

Original entry on oeis.org

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

Views

Author

Takayuki Tatekawa, Apr 12 2024

Keywords

Comments

Constants from generalized Pi integrals: the case of n=14.
In general, for k > 0, Integral_{x=0..1} 1/sqrt(1 - x^k) dx = 2^(2/k) * Gamma(1 + 1/k)^2 / Gamma(1 + 2/k) = 2^(2/k - 1) * Gamma(1/k)^2 / (k*Gamma(2/k)). - Vaclav Kotesovec, Apr 15 2024

Examples

			2.191450245201078533946264870311...

Links

Crossrefs

Cf. A085565, A113477, A262427, A371824.

Programs

  • Maple
    Beta(1/14, 1/2) / 7: evalf(%, 90); # Peter Luschny, Apr 14 2024
  • Mathematica
    RealDigits[Sqrt[Pi]/7*Gamma[1/14]/Gamma[4/7], 10, 5001][[1]]

Formula

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^14).
Equals Beta(1/14, 1/2) / 7. - Peter Luschny, Apr 14 2024
Equals Gamma(1/14)^2 / (7 * 2^(6/7) * Gamma(1/7)). - Vaclav Kotesovec, Apr 15 2024

A371929 Decimal expansion of Pi^(1/2)*Gamma(1/12)/(6*Gamma(7/12)).

Original entry on oeis.org

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

Views

Author

Takayuki Tatekawa, Apr 12 2024

Keywords

Comments

Constants from generalized Pi integrals: the case of n=12.

Examples

			2.2221586039664144669155853439....

Links

Crossrefs

Cf. A085565, A113477, A262427, A371824.

Programs

  • Maple
    Beta(1/12, 1/2) / 6: evalf(%, 89); # Peter Luschny, Apr 14 2024
  • Mathematica
    RealDigits[Sqrt[Pi]/6*Gamma[1/12]/Gamma[7/12], 10, 5001][[1]]
RealDigits[(1 + Sqrt[3]) * Gamma[1/4]^2 / (4 * 3^(3/4) * Sqrt[Pi]), 10, 120][[1]] (* Vaclav Kotesovec, Apr 15 2024 *)

Formula

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^12).
Equals Beta(1/12, 1/2) / 6. - Peter Luschny, Apr 14 2024
Equals (1 + sqrt(3)) * Gamma(1/4)^2 / (4 * 3^(3/4) * sqrt(Pi)). - Vaclav Kotesovec, Apr 15 2024

A372327 Decimal expansion of Pi^(1/2)*Gamma(1/18)/(9*Gamma(5/9)).

Original entry on oeis.org

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

Views

Author

Takayuki Tatekawa, Apr 28 2024

Keywords

Comments

Constant from generalized Pi integrals: the case of n=18.

Examples

			2.14999545849204723391222945664...

Links

Crossrefs

Cf. A085565, A113477, A262427, A371929, A371930.

Programs

  • Mathematica
    RealDigits[Sqrt[Pi]/9*Gamma[1/18]/Gamma[5/9], 10, 5001][[1]]

Formula

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^18).
Equals Gamma(1/18)^2 / (9 * 2^(8/9) * Gamma(1/9)). - Vaclav Kotesovec, Apr 29 2024

A373534 Decimal expansion of Pi^(1/2)*Gamma(1/20)/(10*Gamma(11/20)).

Original entry on oeis.org

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

Views

Author

Takayuki Tatekawa, Jun 08 2024

Keywords

Comments

Constants from generalized Pi integrals: the case of n=20.

Examples

			2.135344933248004228046475279683...

Links

Crossrefs

Cf. A085565, A113477, A262427, A371824, A371881, A371930, A372111, A372327.

Programs

  • Maple
    (2*sqrt(Pi)*GAMMA(21/20))/GAMMA(11/20): evalf(%, 102); # Peter Luschny, Jun 17 2024
  • Mathematica
    RealDigits[2*Sqrt[Pi]/20*Gamma[1/20]/Gamma[11/20], 10, 5001][[1]]

Formula

Equals 2*Integral_{x=0..1} dx/sqrt(1-x^20).
Equals (2*sqrt(Pi)*Gamma(21/20))/Gamma(11/20). - Peter Luschny, Jun 17 2024
Showing 1-5 of 5 results.

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