τ
= √-1 :
k( τ )
= k’( τ )
= 1/√2
⇒
θ3( 0 | τ )^2 = 1/A.G.M.( 1 , k’( τ ) ) = √2/A.G.M.( 1 , √2 )
= ( η( τ )f( τ )^2 )^2
= η( τ )^2f( τ )^4
f( τ )^12
= 2^2/( k( τ )k’( τ ) )
= 2^3
f( τ )^4
= 2
⇒
√2/A.G.M.( 1 , √2 )
= 2η( τ )^2
⇒
η( τ ) = 1/( 2^( 1/4 )√A.G.M.( 1 , √2 ) )
=
exp( -π/12 )( 1-exp( -2π ) )( 1-exp( -4π ) )( 1-exp( -6π ) ) ・・・
=
1/( 2^( 1/4 )√A.G.M.( 1 , √2 ) )
=
0.7682254223 ・・・