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 1-3 of 3 results.

A102521 Decimal expansion of value of Ahmed's 2nd integral.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein, Jan 14 2005

Keywords

Examples

			0.590489270886385075159298139571568463546513361355639...

References

  • Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.

Links

Crossrefs

Cf. A096615, A098459.

Programs

  • Mathematica
    RealDigits[Pi/4 - Pi/Sqrt[2] + (3*ArcTan[Sqrt[2]])/Sqrt[2], 10, 50][[1]] (* G. C. Greubel, Jun 02 2017 *)
  • PARI
    Pi/4 - Pi/sqrt(2) + (3*atan(sqrt(2)))/sqrt(2) \\ G. C. Greubel, Jun 02 2017

Formula

Equals Pi/4 - Pi/sqrt(2) + (3*arctan(sqrt(2)))/sqrt(2).
Equals Integral_{x=0..1} arctan(sqrt(x^2 + 1))/(x^2 + 1)^(3/2) dx (Borwein et al., 2004). - Amiram Eldar, Aug 17 2020

A098459 Decimal expansion of G/2 + (1/8)*Pi*log(2), where G is Catalan's constant (often also denoted K).

Original entry on oeis.org

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

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004

Keywords

Examples

			0.7301810583765597738398878697...

References

  • Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.

Links

Crossrefs

Cf. A006752, A102886, A096615, A102521.

Programs

  • Mathematica
    RealDigits[Catalan/2 + Pi*Log[2]/8, 10 , 100][[1]] (* Amiram Eldar, Aug 17 2020 *)

Formula

Equals Integral_{x=0..1} arctan(x) / (x*(x^2+1)) dx.
From Amiram Eldar, Aug 17 2020: (Start)
Equals (1/2) * A006752 + A102886.
Equals Integral_{x=0..Pi/4} x*cot(x) dx. (End)

A374677 Decimal expansion of (5/96)*Pi^2 - (log(2)^2)/8.

Original entry on oeis.org

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

Views

Author

Paolo Xausa, Jul 16 2024

Keywords

Examples

			0.4539852691502955833142419237860497501646027251778...

Links

Crossrefs

Cf. A096615, A253191, A367053.

Programs

  • Mathematica
    First[RealDigits[5*Pi^2/96 - Log[2]^2/8, 10, 100]]

Formula

Equals A096615 - A253191/8.
Equals Sum_{k >= 1} d(k)/(2^floor((k + 1)/2)*k^2), where d is the periodic sequence {1, 0, -1, -1, -1, 0, 1, 1}. See Bailey et al. (1997), eq. 2.15, p. 907.
Showing 1-3 of 3 results.

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