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.

A216184 Decimal expansion of Integral_{x=0..Infinity} sin(x)/(x^2+1) dx.

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Mar 11 2013

Keywords

Examples

			0.646761122...

References

  • Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 424-425.

Crossrefs

Cf. A086056 (Same integral with cos(x))

Programs

  • Mathematica
    (ExpIntegralEi[1] - E^2*ExpIntegralEi[-1])/(2*E) // RealDigits[#, 10, 100]& // First

A225155 Decimal expansion of Pi/(4*e) + e/(3*Pi).

Original entry on oeis.org

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

Views

Author

Jimmy Zotos, May 01 2013

Keywords

Comments

Approximates Euler Mascheroni constant giving 3 correct decimal places.
The constant is not known to be transcendental, or even irrational. - Balarka Sen, May 06 2013

Examples

			0.5773504972584854585501148923768706139231...

Links

Crossrefs

Cf. A000796, A001113, A061360, A086056, A001620, A225572 (continued fraction).

Programs

  • Magma
    R:= RealField(100); (3*Pi(R)^2 + 4*Exp(2))/(12*Pi(R)*Exp(1)); // G. C. Greubel, Aug 30 2018
  • Mathematica
    RealDigits[(3*Pi^2 + 4*E^2)/(12*E*Pi), 10, 100][[1]] (* G. C. Greubel, Aug 30 2018 *)
  • PARI
    default(realprecision, 1020); x=10*Pi/exp(1)/4+10*exp(1)/Pi/3; d=0; for (n=0, 1000, d=floor(x); x=(x-d)*10; print1(d", ")) \\

Extensions

More terms from Balarka Sen, May 02 2013

A229174 Decimal expansion of Integral_{x=0..Infinity} x*cos(x)/(1+x^2).

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Sep 28 2013

Keywords

Examples

			0.050413760455935997212200091275136109621498785400910367873

References

  • Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 424-425.

Crossrefs

Cf. A216184, A086056.

Programs

  • Mathematica
    Join[{0}, (E^2*ExpIntegralEi[-1] + ExpIntegralEi[1])/(2*E) // RealDigits[#, 10, 106]& // First] (* Jean-François Alcover, Feb 19 2014 *)

Formula

Equals (e^2*Ei(-1)+Ei(1))/(2*e) where Ei is the exponential integral function. - Jean-François Alcover, Feb 19 2014
Showing 1-3 of 3 results.

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

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