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.

Previous Showing 11-19 of 19 results.

A347909 Decimal expansion of Integral_{x=0..1} exp(-x^2) dx.

Original entry on oeis.org

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

Views

Author

Jianing Song, Sep 18 2021

Keywords

Examples

			0.74682413281242702539946743613185300535449968...

Crossrefs

Cf. A019704 (sqrt(Pi)/2 = Integral_{x=0..+oo} exp(-x^2) dx), A002161 (sqrt(Pi) = Integral_{x=-oo..+oo} exp(-x^2) dx).
Cf. A347910 (inverse integrand), A007680.

Programs

  • Mathematica
    RealDigits[(Sqrt[Pi]/2) Erf[1], 10, 91][[1]]
  • PARI
    intnum(x=0, 1, exp(-x^2)) \\ Michel Marcus, Sep 18 2021

Formula

Equals (sqrt(Pi)/2) * erf(1) = (sqrt(Pi)/(2*i)) * erfi(i).
Equals Sum_{k>=0} (-1)^k / ((2*k + 1)*k!). - Ilya Gutkovskiy, Sep 18 2021

A347910 Decimal expansion of Integral_{x=0..1} exp(x^2) dx.

Original entry on oeis.org

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

Views

Author

Jianing Song, Sep 18 2021

Keywords

Examples

			1.462651745907181608804048586856988155...

Crossrefs

Cf. A347909 (inverse integrand), A007680.

Programs

  • Mathematica
    RealDigits[(Sqrt[Pi]/2) Erfi[1], 10, 91][[1]]
  • PARI
    intnum(x=0, 1, exp(x^2)) \\ Michel Marcus, Sep 18 2021

Formula

Equals (sqrt(Pi)/2) * erfi(1) = (sqrt(Pi)/(2*i)) * erf(i).
Equals Sum_{k>=0} 1 / ((2*k + 1)*k!) . - Ilya Gutkovskiy, Sep 18 2021
Equals A019704 * A099288. - R. J. Mathar, Sep 30 2021

A371856 Decimal expansion of Integral_{x=0..oo} exp(-x^5) dx.

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 09 2024

Keywords

Examples

			0.91816874239976061064095165518583040068682...

Links

Crossrefs

Decimal expansion of Integral_{x=0..oo} exp(-x^k) dx: A019704 (k=2), A202623 (k=3), A068467 (k=4), this sequence (k=5), A203126 (k=6), A371857 (k=7), A203125 (k=8).
Cf. A175380.

Programs

  • Mathematica
    RealDigits[Gamma[6/5], 10, 104][[1]]

Formula

Equals Gamma(6/5).
Equals A175380 / 5.

A371857 Decimal expansion of Integral_{x=0..oo} exp(-x^7) dx.

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 09 2024

Keywords

Examples

			0.9354375628925463482448704784898566089...

Links

Crossrefs

Decimal expansion of Integral_{x=0..oo} exp(-x^k) dx: A019704 (k=2), A202623 (k=3), A068467 (k=4), A371856 (k=5), A203126 (k=6), this sequence (k=7), A203125 (k=8).
Cf. A220086.

Programs

  • Mathematica
    RealDigits[Gamma[8/7], 10, 106][[1]]

Formula

Equals Gamma(8/7).
Equals A220086 / 7.

A367549 Decimal expansion of 1 - DawsonF(1/2).

Original entry on oeis.org

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

Views

Author

Peter Luschny, Nov 23 2023

Keywords

Examples

			0.57556361649797770406595764751033042890357052264030796184866030336675484524040...

Links

Crossrefs

Cf. A019704, A092042, A367563.

Programs

  • Maple
    1 - sqrt(Pi/4)*erfi(1/2)/exp(1/4): evalf(%, 109);
  • Mathematica
    N[1 - DawsonF[1/2], 110] // RealDigits // First

Formula

Equals 1 - sqrt(Pi/4) * erfi(1/2) / exp(1/4) = 1 - A019704 * A367563 / A092042.
Let C denote the constant. Then:
2*C - 1 = Sum_{n>=0} (-1)^n / Pochhammer(n, n).
2*(C - 1) = Sum_{n>=1} (-1)^n*Gamma(n) / Gamma(2*n).
Equals Integral_{x=0..oo} exp(-x)*cos(sqrt(x)) dx. - Kritsada Moomuang, Jun 06 2025

A371356 Decimal expansion of Gamma(3/2) * zeta(3/2).

Original entry on oeis.org

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

Views

Author

Peter Luschny, Mar 19 2024

Keywords

Examples

			2.3151573733941170004258194691179813666769281990...

Crossrefs

Cf. A019704, A078434.

Programs

  • Maple
    DecimalExpansion := proc(f, prec)
Digits := prec + 10: evalf(f, Digits) * 10^prec:
ListTools:-Reverse(convert(floor(%), base, 10)) end:
DecimalExpansion(sqrt(Pi/4)*Zeta(3/2), 100);
  • Mathematica
    RealDigits[Pochhammer[1, 1/2] Zeta[3/2, 1], 10, 100][[1]]

Formula

Equals Pochhammer(1, 1/2) * zeta(3/2, 1).
Equals sqrt(Pi/4) * zeta(3/2).
Equals Integral_{x>=0} sqrt(x) / (exp(x) - 1).
Equals A019704 * A078434.

A371534 Decimal expansion of (1/8) * Pi^(3/2).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 10 2024

Keywords

Examples

			0.6960409996039634806606022477648544627517030487854...

Links

Crossrefs

Cf. A003881, A019704, A175476, A222068.

Programs

  • Mathematica
    RealDigits[(1/8) Pi^(3/2), 10, 103][[1]]

Formula

Equals Integral_{x=0..oo, y=0..oo, z=0..oo} exp(-x^2 - y^2 - z^2) dx dy dz.

A371667 Decimal expansion of -Ei(-1) / log(2).

Original entry on oeis.org

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

Views

Author

Ilya Gutkovskiy, Apr 10 2024

Keywords

Examples

			0.316504114203126786893754620753862815669085943...

Crossrefs

Cf. A007525, A019704, A099285, A232734.

Programs

  • Mathematica
    RealDigits[-ExpIntegralEi[-1]/Log[2], 10, 103][[1]]
  • PARI
    eint1(1)/log(2) \\ Michel Marcus, Apr 11 2024

Formula

Equals Integral_{x=0..oo} exp(-2^x) dx.

A380907 Decimal expansion of 1/(2^(1/4)*sqrt(1+Pi/4)).

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Feb 08 2025

Keywords

Examples

			0.62932496342101931026228634377882172549266644...

Links

Crossrefs

Cf. A003881, A010767, A019704, A228497.

Programs

  • Mathematica
    RealDigits[1/(2^(1/4)Sqrt[1+Pi/4]),10,100][[1]]
Previous Showing 11-19 of 19 results.

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