Using the Lagrange’s formula, prove that y0 = 1 2 (y1 + y−1) − 1 8 1 2 (y3 − y1) − 1 2 (y−1 − y−3)

#LagrangesFormula #PartialFractions #Mathematics #Calculus #Algebra #MathHelp #MathTutorial #MathProblemSolving #MathTips #LagrangesTheorem

Using the Lagrange’s formula, prove that
y0 =
1
2
(y1 + y−1) −
1
8

1
2
(y3 − y1) −
1
2
(y−1 − y−3)

.
Note: yi = y(i) = f(i)