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Table 1 Coefficients of the first five Legendre polynomials for adjusted time points (t*) used in the poplar growth study.

From: A joint model for nonparametric functional mapping of longitudinal trajectory and time-to-event

t 0 1 2 3 4 5 6 7 8 9 10
t* -1 -4/5 -3/5 -2/5 -1/5 0 1/5 2/5 3/5 4/5 1
P0(t*) 1 1 1 1 1 1 1 1 1 1 1
P1(t*) -1 -4/5 -3/5 -2/5 -1/5 0 1/5 2/5 3/5 4/5 1
P2(t*) 1 23/50 1/25 -13/50 -11/25 -1/2 -11/25 -13/50 1/25 23/50 1
P3(t*) -1 -2/25 9/25 11/25 7/25 0 -7/25 -11/25 -9/25 2/25 1
P4(t*) 1 -24/103 -51/125 -93/823 29/125 3/8 29/125 -93/823 -51/125 -24/103 1
P5(t*) -1 167/418 107/701 -59/218 -274/891 0 274/891 59/218 -107/701 -167/418 1
P6(t*) 1 -172/439 132/767 163/557 -56/695 -5/16 -56/695 163/557 132/767 -172/439 1
P7(t*) -1 110/459 -10/31 13/891 231/787 0 -231/787 -13/891 10/31 -110/459 1