On the Direct Numerical Calculation of Elliptic Functions and Integrals

Originally published in 1924, this book presents an account regarding the direct numerical calculation of elliptic functions and integrals.

Louis V. King (Author)

9781316612729, Cambridge University Press

Paperback / softback, published 28 July 2016

52 pages
20.4 x 13.4 x 0.4 cm, 0.08 kg

Originally published in 1924, this book presents an account regarding the direct numerical calculation of elliptic functions and integrals. Notes are incorporated and an appendix section containing examples is also included. This book will be of value to anyone with an interest in the history of mathematics.

Preface
1. Introduction
2. Historical note on Landen's transformation and the various scales of moduli and amplitudes
3. On the scale of arithmetico-geometrical means
4. Landen's scale of increasing amplitudes
5. The hyperbolic scale of increasing amplitudes
6. Gauss' scale of increasing amplitudes
7. Landen's scale of decreasing amplitudes
8. The hyperbolic scale of decreasing amplitudes
9. On the numerical computation of the third elliptic integral
10. Note on the calculation of the third elliptic integral in terms of the complementary A. G. M. scale
Summary of formulae
Appendix. Examples 1-35.

Subject Areas: History of mathematics [PBX]