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Year 2 of the mathematics course of the University of Oxford

Options II course of the University of Oxford

Past exam of the options II course of the University of Oxford

2012

Differentiate the <power series> twice and align the <coefficient> of $\xi^k$. The equation becomes
$$
(k+2)(k+1)a_{k+2}+(\epsilon-1-2k)a_k=0\qquad(k\geq0).
$$
Thus
$$
\boxed{a_{k+2}=\frac{2k+1-\epsilon}{(k+2)(k+1)}a_k.}
$$
Even <coefficients> are generated from $a_0$, and odd <coefficients> from $a_1$; the two <parity> <sequences> are <independent>.

Solution

Past exam of the options II course of the University of Oxford / 2012 / J / J2 / a / ii / Solution

Past exam of the options II course of the University of Oxford / 2012 / J / J2 / a / ii / Solution

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Past exam of the options II course of the University of Oxford / 2012 / J / J2 / a / ii / Solution

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