τ → q

k

= 1/k’

⇨

K’( k )

= ( 2/( 1+k ) )K( ( 1-k )/( 1+k ) ) : Landen

= k’K( k )

⇨

τ

= K’( k )√-1/K( k )

= k’√-1

= ( 1+√-3 )/2

⇨

q

= exp( π√-1τ)

= exp( -√-3π/2 )√-1

1/q

〜 ( 4/k )^2-8 : Jacobi

に代入して・・・