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.

A367960 Decimal expansion of tanh(Pi/2).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Dec 06 2023

Keywords

Examples

			0.91715233566727434637309...

References

  • Calvin C. Clawson, Mathematical Mysteries: The Beauty and Magic of Numbers, Springer, 2013. See p. 225.

Crossrefs

Cf. A367961, A367959, A308715, A083124 (cont. frac).

Programs

  • Maple
    evalf(tanh(Pi/2)) ;
  • Mathematica
    First[RealDigits[Tanh[Pi/2],10,100]] (* Paolo Xausa, Dec 06 2023 *)

Formula

Equals 1/A367961 = A367959 / A308715 = (2/Pi)*A228048.
Equals (e^Pi - 1)/(e^Pi + 1) = K_{n>0} Pi^(2-[n=1])/(4*n - 2) (see Clawson at p. 225). - Stefano Spezia, Jul 01 2024

A367961 Decimal expansion of coth(Pi/2).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Dec 06 2023

Keywords

Examples

			1.090331410727368230030...

Crossrefs

Cf. A367960, A308715, A367959.

Programs

  • Maple
    evalf(coth(Pi/2)) ;
  • Mathematica
    First[RealDigits[Coth[Pi/2],10,100]] (* Paolo Xausa, Dec 06 2023 *)

Formula

Equals 1/A367960 = A308715 / A367959.

A369880 Decimal expansion of sinh(Pi/2)/(Pi/2)^2.

Original entry on oeis.org

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

Views

Author

Amiram Eldar, Feb 04 2024

Keywords

Examples

			0.93268131478635101777369755780799023506619209387697...

References

  • József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 424.

Links

Crossrefs

Cf. A000120, A019669, A060294, A096111, A091476, A185199, A258232, A308716, A367959.

Programs

  • Mathematica
    RealDigits[Sinh[Pi/2]/(Pi/2)^2, 10, 120][[1]]
  • PARI
    sinh(Pi/2)/(Pi/2)^2

Formula

Equals A060294 * A308716 = A308716 / A019669 = A185199 * A367959 = A367959 / A091476 = A367959 / A019669^2.
Equals Sum_{k>=0} (-1/16)^A000120(k)/D(k)^4, where D(k) = A096111(k-1) for k >= 1, and D(0) = 1 (Borwein and Borwein, 1992).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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