James Stirling’s Methodus Differentialis

An Annotated Translation of Stirling’s Text

  • Ian Tweddle

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Introduction

    1. Ian Tweddle
      Pages 1-13
  3. Methodus Differentials: Sive Tractatus De Summatione Et Interpolatione Seriesum Infinitarum / The method of Differences: or a Treatise on Summation and Interpolation of Infinite Series

    1. Front Matter
      Pages 15-18
    2. Ian Tweddle
      Pages 33-100
    3. Ian Tweddle
      Pages 101-283
    4. Ian Tweddle
      Pages 289-292
  4. Back Matter
    Pages 284-296

About this book


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.


Acceleration of convergence Analysis History of Mathematics Interpolation Stirling numbers Stirling's formula numerical analysis

Authors and affiliations

  • Ian Tweddle
    • 1
  1. 1.Department of MathematicsUniversity of StrathclydeGlasgowUK

Bibliographic information