This site is supported by donations to The OEIS Foundation.

Template:Sequence of the Day for August 17

From OeisWiki
Jump to: navigation, search


Intended for: August 17, 2011

Timetable

  • First draft entered by Alonso del Arte on May 29, 2011 as a verbatim copy of the write-up from December 17, 2010 ✓
  • Draft reviewed by Alonso del Arte on July 16, 2011
  • Draft approved by Daniel Forgues on July 20, 2011
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A014549: Gauß’s constant
2
π
1
0
1
2  1  −  x 4
dx
.
0.834626841674...
This is the reciprocal of the arithmetic-geometric mean of 1 and
2  2
. It was on May 30, 1799 that Carl Friedrich Gauß discovered the integral for this number shown above.

Its simple continued fraction is (see A053002)

     
1
M  (1,
2  2
 )
 = 
1
1 + 
1
5 + 
1
21 + 
1
3 + 
1
4 + 
1
14 + 
1
 .