19 Sep
2018
19 Sep
'18
9:11 p.m.
World's smallest(?) fibonacci formula: F_n+1 = U_n(i/2)/i^n. where U:= Чебышёв polynomial, 2nd kind := sin((n+1)acos z)/√(1-z)/√(1+z). This provides an alternate (complex) interpolation for nonintegers. Slightly nonobvious: With this definition, Im(F_x+1)/Im(F_x) = -1/GoldenRatio (x real noninteger), which can be coaxed out of Mathematica. —rwg