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 11-15 of 15 results.

A256615 Decimal expansion of log(Gamma(1/24)).

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Apr 04 2015

Keywords

Examples

			3.155402877381144722774664455739805690458351588844024...

Links

Crossrefs

Cf. decimal expansions of log(Gamma(1/k)): A155968 (k=2), A256165 (k=3), A256166 (k=4), A256167 (k=5), A255888 (k=6), A256609 (k=7), A255306 (k=8), A256610 (k=9), A256612 (k=10), A256611 (k=11), A256066 (k=12), A256614 (k=16), A256616 (k=48).

Programs

  • Maple
    evalf(log(GAMMA(1/24)),100);
  • Mathematica
    RealDigits[Log[Gamma[1/24]],10,100][[1]]
  • PARI
    log(gamma(1/24))

A256616 Decimal expansion of log(Gamma(1/48)).

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, Apr 04 2015

Keywords

Examples

			3.859529085168528678772669493173125038058701527316499...

Links

Crossrefs

Cf. decimal expansions of log(Gamma(1/k)): A155968 (k=2), A256165 (k=3), A256166 (k=4), A256167 (k=5), A255888 (k=6), A256609 (k=7), A255306 (k=8), A256610 (k=9), A256612 (k=10), A256611 (k=11), A256066 (k=12), A256614 (k=16), A256615 (k=24).

Programs

  • Maple
    evalf(log(GAMMA(1/48)),100);
  • Mathematica
    RealDigits[Log[Gamma[1/48]],10,100][[1]]
  • PARI
    log(gamma(1/48))

A257958 Decimal expansion of the Digamma function at 1/Pi, negated.

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, May 14 2015

Keywords

Comments

The reference gives an interesting series representation with rational coefficients for Psi(1/Pi) = -log(Pi) - Pi/2 - 1/2 - 1/8 - 1/72 + 1/64 +7/400 + 7/576 + 643/94080 + 103/30720 + ...

Examples

			-3.2902139601732240908430908455400190374021932820070161...

Links

Crossrefs

Cf. A257955, A257957, A257959, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.

Programs

  • Maple
    evalf(Psi(1/Pi), 120);
  • Mathematica
    RealDigits[PolyGamma[1/Pi], 10, 120][[1]]
  • PARI
    default(realprecision, 120); psi(1/Pi)

Formula

Int_0^infinity x*dx/[(x^2+1)(exp(2x)-1)] = -Pi/2-Psi(1/Pi) = -1.5707...+ 3.2902.. = 1.71941... - R. J. Mathar, Aug 14 2023

A257959 Decimal expansion of the Digamma function at 1/2 + 1/Pi, negated.

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, May 14 2015

Keywords

Comments

The reference gives an interesting series representation with rational coefficients for Psi(1/2 + 1/Pi) = -log(Pi) + 1/4 + 1/16 - 5/576 - 13/512 - 569/25600 -539/36864 - 98671/12042240 - 16231/3932160 - ...

Examples

			-0.9236326759613377346000263347486747139894893215261027...

Links

Crossrefs

Cf. A257955, A257957, A257958, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.

Programs

  • Maple
    evalf(Psi(1/2+1/Pi), 120);
  • Mathematica
    RealDigits[PolyGamma[1/2+1/Pi], 10, 120][[1]]
  • PARI
    default(realprecision, 120); psi(1/2+1/Pi)

A257957 Decimal expansion of log(Gamma(1/Pi)).

Original entry on oeis.org

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

Views

Author

Iaroslav V. Blagouchine, May 14 2015

Keywords

Comments

The reference gives an interesting series representation with rational coefficients for log(Gamma(1/Pi)) = (1-1/Pi)*log(Pi) - 1/Pi + log(2)/2 + (1 + 1/4 + 1/12 + 1/32 + 1/75 + 1/144 + 13/2880 + 157/46080 + ...)/(2*Pi).
The value log(Gamma(1/Pi)) is also intimately related to integral_{x=0..1} arctan(arctanh(x))/x (A257963).

Examples

			1.0336461257655827064855374553316178667100308701595988...

Links

Crossrefs

Cf. A257955, A257963, A257958, A257959, A155968, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616.

Programs

  • Maple
    evalf(log(GAMMA(1/Pi)), 120);
  • Mathematica
    RealDigits[Log[Gamma[1/Pi]], 10, 120][[1]]
  • PARI
    default(realprecision, 120); log(gamma(1/Pi))
Previous Showing 11-15 of 15 results.

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