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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A Common Question in Calculus<br />
Can we determine the interval <strong>of</strong> convergence <strong>of</strong> a <strong>Taylor</strong><br />
series corresponding to a function f simply by looking at f<br />
itself?<br />
0.8<br />
0.7<br />
0.6<br />
f(x) = 1<br />
x 2 + 4<br />
y<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
–2 –1 0<br />
1 2<br />
x<br />
<strong>Taylor</strong> <strong>Series</strong> <strong>are</strong><strong>Limits</strong> <strong>of</strong> <strong>Legendre</strong> <strong>Expansions</strong> – p.2/15
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