τ
= ( -1+√-t )/2 ( t ＞ 0 ) :
k( √-t )
= sinθ
k’( √-t )
= cosθ
⇒
k’( τ )
= cos2θ-√-1sin2θ
K( k( τ ) )
= K( sinθ )( cosθ+√-1sinθ ) : 極形式
K( sinθ )
= ∫ 1/√( 4t( 1-tcos2θ )( 1+( tsin2θ )^2 ) ) dt
( t = 0 〜 1/cos2θ )
= ( 1/( 2√cos2θ ) )∫ 1/√( x( 1-x )( 1+( xtan2θ )^2 ) ) dx
( x = 0 〜 1 )