|
Search: id:A102753
|
|
|
| A102753 |
|
Decimal expansion of (Pi^2)/2. |
|
+0
8
|
|
| 4, 9, 3, 4, 8, 0, 2, 2, 0, 0, 5, 4, 4, 6, 7, 9, 3, 0, 9, 4, 1, 7, 2, 4, 5, 4, 9, 9, 9, 3, 8, 0, 7, 5, 5, 6, 7, 6, 5, 6, 8, 4, 9, 7, 0, 3, 6, 2, 0, 3, 9, 5, 3, 1, 3, 2, 0, 6, 6, 7, 4, 6, 8, 8, 1, 1, 0, 0, 2, 2, 4, 1, 1, 2, 0, 9, 6, 0, 2, 6, 2, 1, 5, 0, 0, 8, 8, 6, 7, 0, 1, 8, 5, 9, 2, 7, 6, 1, 1, 5, 9, 1, 2, 0, 1
(list; cons; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Equals psi_1(1/2), where psi_1(x) is the second logarithmic derivative of GAMMA(x).
Also equals the volume of revolution of the sine or cosine curve for one half period, Integral_{0,Pi} Sin(x)^2 dx. - Robert G. Wilson v Dec 15 2005.
Equals sum_{k=1..infinity} 2^(2k)/k^2/binomial(2k,k) [Amdeberhan]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 28 2007
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of Mathworld.
T. Amdeberhan, L. Medina, V. H. Moll, The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals, arXiv:0705.2379, equation 2.39.
|
|
EXAMPLE
|
4.9348022005446793094172454999380755676568497036203953132066746881100\
224112096026215008867018592761159120129568870115720388....
|
|
MATHEMATICA
|
RealDigits[Pi^2/2, 10, 111][[1]] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 15 2005)
|
|
CROSSREFS
|
Cf. A002388.
Sequence in context: A021957 A096301 A159628 this_sequence A120869 A070436 A070435
Adjacent sequences: A102750 A102751 A102752 this_sequence A102754 A102755 A102756
|
|
KEYWORD
|
cons,nonn
|
|
AUTHOR
|
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 10 2005
|
|
|
Search completed in 0.002 seconds
|
