Taylor Series are Limits of Legendre Expansions - Gvsu - Grand ...
Taylor Series are Limits of Legendre Expansions - Gvsu - Grand ...
Taylor Series are Limits of Legendre Expansions - Gvsu - Grand ...
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The Pro<strong>of</strong><br />
• By <strong>Taylor</strong>’s Theorem,<br />
f(th) = f(0)+f ′ (0)th+...+ f(n) (0)<br />
n!<br />
(th) n +O ( h n+1) as h → 0.<br />
<strong>Taylor</strong> <strong>Series</strong> <strong>are</strong><strong>Limits</strong> <strong>of</strong> <strong>Legendre</strong> <strong>Expansions</strong> – p.10/15
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