## James Stirling’s Methodus Differentialis: An Annotated Translation of Stirling’s TextJames Stirling's "Methodus Differentialis" is one of the early classics of numerical analysis. It contains not only the results and ideas for which Stirling is chiefly remembered, for example, Stirling numbers and Stirling's asymptotic formula for factorials, but also a wealth of material on transformations of series and limiting processes. An impressive collection of examples illustrates the efficacy of Stirling's methods by means of numerical calculations, and some germs of later ideas, notably the Gamma function and asymptotic series, are also to be found. This volume presents a new translation of Stirling's text that features an extensive series of notes in which Stirling's results and calculations are analysed and historical background is provided. Ian Tweddle places the text in its contemporary context, but also relates the material to the interests of practising mathematicians today. Clear and accessible, this book will be of interest to mathematical historians, researchers and numerical analysts. |

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### Contents

Introduction | 1 |

Some Mathematical Points | 5 |

2 Inverse Factorial Series | 6 |

3 Stirlings Summation Procedure | 7 |

4 Error Bounds | 8 |

5 Notation and Terminology | 9 |

6 Checking Stirlings Calculations | 10 |

Stirlings Principal Calculations | 11 |

On Series Which Converge More Rapidly | 34 |

On Successive Sums | 35 |

Proposition 1 | 37 |

On the Interpolation of Series | 101 |

Proposition 16 | 102 |

On the Differences of Quantities | 110 |

On the Description of Curves Through Given Points | 111 |

Proposition 19 | 112 |

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James Stirling’s Methodus Differentialis: An Annotated Translation of ... Ian Tweddle Limited preview - 2012 |

James Stirling’s Methodus Differentialis: An Annotated Translation of ... Ian Tweddle No preview available - 2012 |