James Stirling’s Methodus Differentialis: An Annotated Translation of Stirling’s Text

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Springer Science & Business Media, Sep 2, 2003 - Mathematics - 296 pages
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James 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

Preface
17
INTRODUCTION
19
On Difference Equations Which Define Series
21
On the Form and Reduction of Series
23
On the Summation of Series
33
Notes
169
Stirlings Letter to De Moivre Dated 19 June 1729
285
References
289
Index
293
Copyright

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Page 290 - Phoronomia sive de Viribus et Motibus Corporum solidorum et fluidorum, libri duo, 1716

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