A numerical tour of wave propagation |

The Taylor expansion of a function at is written as

(10) |

A popular example is

(11) |

Here we mainly consider the following expansion formula:

The Páde expansion of Eq. (12) follows from expansion in continuous fractions:

(13) |

I provide an informal derivation:

The 1st-order Pade expansion is:

(14) |

The 2nd-order Pade expansion is:

(15) |

And the 3rd-order one is:

(16) |

A numerical tour of wave propagation |

2021-08-31