Thiele's interpolation formula: Difference between revisions
Completed restoration of formulae made invisible at 18:05, 31 July 2016 (one ρ character, and three π characters restored today)
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(Completed restoration of formulae made invisible at 18:05, 31 July 2016 (one ρ character, and three π characters restored today)) |
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:: <big><big><math> f(x) = f(x_1) + \cfrac{x-x_1}{\rho_1(x_1,x_2) + \cfrac{x-x_2}{\rho_2(x_1,x_2,x_3) - f(x_1) + \cfrac{x-x_3}{\rho_3(x_1,x_2,x_3,x_4) - \rho_1(x_1,x_2) + \cdots}}} </math></big></big>
<big><big><math>
:: <big><big><math>\rho_1(x_0, x_1) = \frac{x_0 - x_1}{f(x_0) - f(x_1)}</math></big></big>
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# Using columns from this table define an inverse - using Thiele's interpolation - for each trig function;
# Finally: demonstrate the following well known trigonometric identities:
#* <big><big> 6 × sin<sup>-1</sup> ½ = <math>
#* <big><big> 3 × cos<sup>-1</sup> ½ = <math>
#* <big><big> 4 × tan<sup>-1</sup> 1 = <math>
<br><br>
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