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.

A261804 Decimal expansion of zeta(7/2).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Sep 01 2015

Keywords

Comments

Zeta(7/2) appears in the expression of the 8th Madelung constant (A261805).

Examples

			1.126733867317056646427812491854984272221996957403602963842396...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

Links

Crossrefs

Cf. A059750, A078434, A247041, A261805.

Programs

A264156 Decimal expansion of M_5, the 5-dimensional analog of Madelung's constant (negated).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Nov 06 2015

Keywords

Examples

			-1.9093378156187685595201437984336...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

Links

Crossrefs

Cf. A088537, A085469, A090734, A247040, A261805, A264157.

Programs

  • Mathematica
    digits = 32; f[n_, x_] := 1/Sqrt[Pi*x]*(EllipticTheta[4, 0, Exp[-x]]^n - 1); M[5] = NIntegrate[f[5, x], {x, 0, Infinity}, WorkingPrecision -> digits + 5]; RealDigits[M[5], 10, digits] // First

Formula

Equals (1/sqrt(Pi))*Integral_{t=0..oo} ((Sum_{k=-oo..oo} (-1)^k*exp(-k^2*t))^5 - 1)/sqrt(t) dt.

A264157 Decimal expansion of M_7, the 7-dimensional analog of Madelung's constant (negated).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, Nov 06 2015

Keywords

Examples

			-2.01240598979798606439503063580430044165678065812192932878490469117330...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

Links

Crossrefs

Cf. A088537, A085469, A090734, A247040, A261805, A264156.

Programs

  • Mathematica
    digits = 32; f[n_, x_] := 1/Sqrt[Pi*x]*(EllipticTheta[4, 0, Exp[-x]]^n - 1); M[7] = NIntegrate[f[7, x], {x, 0, Infinity}, WorkingPrecision -> digits + 5]; RealDigits[M[7], 10, digits] // First
  • PARI
    th4(x)=1+2*sumalt(n=1,(-1)^n*x^n^2)
intnum(x=0,[oo,1], (th4(exp(-x))^7-1)/sqrt(Pi*x)) \\ Charles R Greathouse IV, Jun 06 2016

Formula

Equals (1/sqrt(Pi))*Integral_{t=0..oo} ((Sum_{k=-oo..oo} (-1)^k*exp(-k^2*t))^7-1)/sqrt(t) dt.

Extensions

More terms from Charles R Greathouse IV, Jun 06 2016
Showing 1-3 of 3 results.

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