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

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Springer Science & Business Media, 2 de set. 2003 - 296 pàgines

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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Continguts

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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Frases i termes més freqüents

A₁ abscissa ai+1 approximately asymptote beginning Bernoulli binomial common interval convergent series corresponding curve decimal places defined denominators denote determined difference equation distance equal equidistant ordinates error Example 2 Let expression factors finite fluent formula give given Hence hyperbola hypergeometric series indeterminate infinite series infinity initial terms intermediate terms interpolation inverse factorial series latter logarithms Methodus Differentialis middle coefficient Moivre multiplied Newton's note on Proposition number of terms obtained ordinates parabola partial sums polynomial positive integer precision arithmetic principal terms produces Proposition 20 quadrature quadruple precision quantity r+s+t recurrence relation result root Scholion semicircumference sequence series S2 solution square Stirling's calculated substituted subtracted successive sums successive values summable summation T₁ T₂ theorem transformed series ultimate relation Wolfgang Pauli write zero

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Pàgina 290 - Phoronomia sive de Viribus et Motibus Corporum solidorum et fluidorum, libri duo, 1716‎
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Informació bibliogràfica

TítolJames Stirling’s Methodus Differentialis: An Annotated Translation of Stirling’s Text
Sources and Studies in the History of Mathematics and Physical Sciences
AutorIan Tweddle
Edicióil·lustrada, anotada
EditorSpringer Science & Business Media, 2003
ISBN1852337230, 9781852337230
Nre. de pàgines296 pàgines
  
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