(D.8) |

where

Here, use has been made of Equation (D.5). Now, to first order in , Equation (D.6) can be inverted to give

(D.10) |

Hence, to the same order, Equation (D.9) gives

(D.11) |

Making use of Equation (3.42), we deduce that, to first order in ,

(D.12) | ||||||

and | (D.13) |

with all of the other zero.

The analysis of Section 3.4, combined with the previous two equations, also implies that

(D.14) |

where

and

Now, to first order in , we can write

where

(D.18) |

Substitution of Equation (D.17) into Equations (D.15) and (D.16), followed by an expansion to first order in , yields

(D.19) |

where

(D.20) |

and

(D.21) |

Here, we have integrated the last two terms in curly brackets by parts.