Gauss

Also known under this formula.
1/2*Pi^(3/2)/GAMMA(3/4)^2*2^(1/2);

Also known under the same number divided by sqrt(2)--> 1.854...

See D.H. Lehmer The Lemniscate Constant : MTAC (or now MOC) vol 3. pp 550-551 (1948-49). or Abramowitz and Stegun, Handbook of Mathematical Functions, p 658 formula 18.14.7 Dover Publication, New York 1964.

2.6220575542921198104648395898911194136827549514316231628168217038007905870704 142502302955329614290934461357526717832180556089569013939356947011194347752358 404226414971649069519368999799321460723831213908102062218974296008565545397723 05369549710288888325525