12 Nov
2009
12 Nov
'09
4:33 p.m.
* Henry Baker <hbaker1@pipeline.com> [Nov 13. 2009 08:29]:
[...]
The real part of cbrt(a'+b'i) is cos(acos(a')/3), which looks like Chebyshev 1/3. Are there Chebyshev functions with non-integral n?
yes, take T_n(x) = cos( n*acos(x) ) or (hypergeometric 2F1) T_n(x) = F( -n, +n; 1/2; x ) Note that T_n( T_{1/n}( x ) ) == x (because T_n( T_m( x ) ) == T_{n*m}(x) )
[...]