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 1-2 of 2 results.

A194655 Decimal expansion of Pi*(Pi^2*zeta(3) + 6*zeta(5))/8.

Original entry on oeis.org

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

Views

Author

Seiichi Kirikami, Aug 31 2011

Keywords

Comments

The absolute value of Integral_{x=0..Pi/2} x^2*(log(2*cos(x)))^3 dx.
The absolute value of d^3/db^3(d^2/da^2(Integral_{x=0..Pi/2} cos(ax)*(2*cos(x))^b dx))).
The absolute value of m=2 and n=3 of (Pi/2)*(d^n/db^n(d^m/da^m(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1)))). [Seiichi Kirikami and Peter J. C. Moses]

Examples

			Equals 7.1021170790001686158...

References

  • I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9

Crossrefs

Cf. A152584, A193712, A193713, A194655.

Programs

  • Mathematica
    RealDigits[ N[Pi (Pi^2*Zeta(3)+6*Zeta(5))/8, 150]][[1]]

Formula

Equals A000796*(A002388*A002117 + 6*A013663)/8.

A193713 Decimal expansion of 11*Pi^5/1440.

Original entry on oeis.org

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

Views

Author

Seiichi Kirikami, Aug 31 2011

Keywords

Comments

The value of Integral_{x=0..Pi/2} x^2*(log(2*cos(x)))^2 dx.
The absolute value of (d^2/db^2(d^2/da^2(Integral_{x=0..Pi/2} cos(a*x)*(2*cos(x))^b dx.
The value of Pi/2*(d^2/db^2(d^2/da^2(gamma(b+1)/gamma((b+a)/2+1)/gamma((b-a)/2+1)))) at a=0 and b=0. [Seiichi Kirikami and Peter J. C. Moses]

Examples

			2.3376503698875666568...

References

  • I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.631.9

Links

Crossrefs

Cf. A152584, A193712, A194655.

Programs

  • Mathematica
    RealDigits[ N[11 Pi^5/1440, 150]][[1]]

Formula

Equals 11*A092731/1440.
Showing 1-2 of 2 results.

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

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