Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 302 / 2 / viii

Table of contents
- Solution viii

Solution

Differentiate the identity in part vi with respect to

y^{t}

, multiply by

μ_{a}^{s} (y) μ_{b}^{t} (y)

, and use

λ μ = I

. The product rule gives

μ_{a}^{s} μ_{b}^{t} \frac{\partial ^{2} z ^{r}}{\partial y ^{s} \partial y ^{t}} = μ_{a}^{s} [T_{b} λ_{s}^{c}] μ_{c}^{r} (z) + T_{b} (z) μ_{a}^{r} (z) .

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