■iのiのi乗について(その8)

sin(sinx)のフーリエ級数展開(近似関数)は

7/8・sinx+1/24・sin3x

sin(sin15°)〜7/8・sinx+1/24・sin3x

sin15°=(2+√3)/(√6+√2)=(√6−√2)/4

より

sin(sin15°)〜7/8・(√6−√2)/4+1/24・√2/2

=21/96・(√6−√2)+2√2/96=(21√6−19√2)/96

===================================

sin(sin(sinx))のフーリエ級数展開(近似関数)は

13/16・sinx+5/96・sin3x+1/150・sin5x

115/144・sinx+29/480・sin3x+1/288・sin5x+1/2520・sin7x

===================================

sin(sin(sin(sinx)))のフーリエ級数展開(近似関数)は

554897/737280・sinx+1555/24576・sin3x+29273/2580480・sin5x-493/2064384・sin7x+2873/10321920・sin9x

===================================