login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102887 Decimal expansion of Integral_{x=0..1} log(gamma(x))^2 dx. 5
1, 8, 6, 6, 3, 1, 7, 0, 8, 3, 7, 9, 3, 5, 6, 2, 0, 8, 0, 9, 9, 2, 9, 6, 7, 9, 3, 7, 9, 7, 8, 2, 8, 9, 7, 3, 9, 8, 0, 0, 4, 0, 4, 1, 8, 6, 7, 9, 5, 3, 3, 8, 8, 0, 9, 4, 0, 5, 5, 1, 4, 4, 9, 5, 9, 3, 0, 4, 0, 9, 6, 5, 9, 8, 4, 9, 0, 5, 6, 3, 0, 3, 4, 7, 5, 5, 2, 3, 9, 8, 6, 0, 2, 9, 2, 5, 7, 2, 5, 0, 8, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also equals 1/6*log(2*Pi)^2 +2*log(A)*log(2*Pi) -1/6*gamma*log(2*Pi) +Pi^2/48 +2*gamma*log(A) +zeta''(2)/(2*Pi^2) (with A the Glaisher-Kinkelin constant). - Jean-Fran├žois Alcover, Apr 29 2013

REFERENCES

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 236.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Equals gamma^2/12 + Pi^2/48 + (gamma*log(2*Pi))/6 + log(2*Pi)^2/3 - ((gamma + log(2*Pi))*zeta'(2))/Pi^2 + zeta''(2)/(2*Pi^2).

EXAMPLE

1.8663170837935620809929679379782897398...

MATHEMATICA

EulerGamma^2/12 + Pi^2/48 + (EulerGamma*Log[2*Pi])/6 + Log[2*Pi]^2/3 - ((EulerGamma + Log[2*Pi])*Zeta'[2])/Pi^2 + Zeta''[2]/(2*Pi^2)

PROG

(PARI) intnum(x=0, 1, log(gamma(x))^2) \\ Michel Marcus, Aug 27 2015

CROSSREFS

Cf. A001620, A074962, A075700, A201994.

Sequence in context: A270137 A269846 A316136 * A067970 A003675 A254290

Adjacent sequences:  A102884 A102885 A102886 * A102888 A102889 A102890

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jan 15 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)