GNU Scientific Library – Reference Manual: Complex Number References and Further Reading

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### 5.9 References and Further Reading

The implementations of the elementary and trigonometric functions are based on the following papers,

- T. E. Hull, Thomas F. Fairgrieve, Ping Tak Peter Tang, “Implementing Complex Elementary Functions Using Exception Handling”, ACM Transactions on Mathematical Software, Volume 20 (1994), pp 215–244, Corrigenda, p553
- T. E. Hull, Thomas F. Fairgrieve, Ping Tak Peter Tang, “Implementing the complex arcsin and arccosine functions using exception handling”, ACM Transactions on Mathematical Software, Volume 23 (1997) pp 299–335

The general formulas and details of branch cuts can be found in the following books,

- Abramowitz and Stegun, Handbook of Mathematical Functions, “Circular Functions in Terms of Real and Imaginary Parts”, Formulas 4.3.55–58, “Inverse Circular Functions in Terms of Real and Imaginary Parts”, Formulas 4.4.37–39, “Hyperbolic Functions in Terms of Real and Imaginary Parts”, Formulas 4.5.49–52, “Inverse Hyperbolic Functions—relation to Inverse Circular Functions”, Formulas 4.6.14–19.
- Dave Gillespie, Calc Manual, Free Software Foundation, ISBN 1-882114-18-3