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.

A076417 Decimal expansion of first solution of equation cos(x)*cosh(x) = -1.

Original entry on oeis.org

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

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Author

Zak Seidov, Oct 10 2002

Keywords

Comments

This is an equation related to a cantilever beam: cos(x)*cosh(x) = -1. The first three solutions are: 1.875 (this sequence), 4.69409 (A076418) and 7.854757 (A076419).

Examples

			1.87510406871196116644530824107821416257011173353...

Links

Crossrefs

Cf. A009398, A076418, A076419.
Cf. A005981, A058258, A008775.

Programs

  • Mathematica
    RealDigits[x/.FindRoot[Cos[x]Cosh[x]==-1,{x,1.8}, WorkingPrecision->120], 10,120][[1]] (* Harvey P. Dale, Jul 24 2011 *)
  • PARI
    solve(x=1, 2, cos(x)*cosh(x) + 1) \\ Michel Marcus, Sep 11 2019

A024277 E.g.f.: log(1+tanh(x)*tan(x))/2 (even powers only).

Original entry on oeis.org

0, 1, -6, 176, -8176, 691456, -86186496, 15358324736, -3667315849216, 1135407181398016, -441731548179726336, 211079248633366839296, -121507103129359646457856, 82940335057202543199256576
Offset: 0

Views

Author

R. H. Hardin

Keywords

Examples

			log(1+tanh(x)*tan(x))/2 = 1/2*x^2 - 1/4*x^4 + 11/45*x^6 - 73/360*x^8 +- ... .

Crossrefs

Cf. A009398.
Cf. A101921.

Programs

  • Mathematica
    Log[ 1+Tanh[ x ]*Tan[ x ]]/2 (* Even Part *)

Extensions

Extended with signs Mar 1997

A296623 Expansion of e.g.f. log(1 + arctan(x)*arctanh(x)) (even powers only).

Original entry on oeis.org

0, 2, -12, 448, -21728, 2380032, -318185472, 69695846400, -18235768762368, 6697099792220160, -2892199532135841792, 1606188416621920911360, -1034069421398404544593920, 810882197441673837894696960, -727447103613537543910242385920, 766865924510666637669136261447680
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 17 2017

Keywords

Examples

			log(1 + arctan(x)*arctanh(x)) = 2*x^2/2! - 12*x^4/4! + 448*x^6/6! - 21728*x^8/8! + 2380032*x^10/10! - 318185472*x^12/12! + ...

Crossrefs

Cf. A009272, A009398, A010050, A012727, A110708, A202139.

Programs

  • Mathematica
    nmax = 15; Table[(CoefficientList[Series[Log[1 + ArcTan[x] ArcTanh[x]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
nmax = 15; Table[(CoefficientList[Series[Log[1 + (I/4) (Log[1 - I x] - Log[1 + I x]) (Log[1 + x] - Log[1 - x])], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

Formula

E.g.f.: log(1 + (i/4)*(log(1 - i*x) - log(1 + i*x))*(log(1 + x) - log(1 - x))), where i is the imaginary unit (even powers only).
Showing 1-3 of 3 results.

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