K( cos( π/12 ) ) ∈ ( 2.74707 , 2.82075 )
= ( 3^( 1/4 )/2 )B( 1/3 , 1/2 )
= 2.7681 ・・・
更に
K( cos( π/12 ) )
= ( π/2 )( 1/A.G.M.( 1 , sin( π/12 ) ) )
= 2.7680631454 ・・・
⇒
B( 1/3 , 1/2 )
= ( 1/3^( 1/4 ) )( π/A.G.M.( 1 , sin( π/12 ) ) )
= 4.2065463162 ・・・
Remark :
K( cos( π/12 ) )
= B( 1/6 , 1/2 )/( 2( 3^( 1/4 ) )
⇒
B( 1/6 , 1/2 )
= 3^( 1/4 )( π/A.G.M.( 1 , sin( π/12 ) ) )
= 7.2859519439 ・・・