Chapter 4 Elementary Functions

R. Roy Department of Mathematics and Computer Science, Beloit College, Beloit, Wisconsin. F. W. J. Olver Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland.

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Acknowledgements:

The authors are grateful to Steven G. Krantz and Peter R. Turner for advice on early drafts of this chapter.

Notes:

The main references used in writing this chapter are Levinson and Redheffer (1970), Hobson (1928), Wall (1948), and Whittaker and Watson (1927). For additional bibliographic reading see Copson (1935) and Silverman (1967).

Referenced by:

Profile Frank W. J. Olver, Profile Ranjan Roy, Profile Ranjan Roy, § ‣ Chapter Authors, § ‣ Chapter Authors, § ‣ Associate Editors, § ‣ Software Cross Index

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• Notation
  1. 4.1 Special Notation
• Logarithm, Exponential, Powers
  1. 4.2 Definitions
  2. 4.3 Graphics
  3. 4.4 Special Values and Limits
  4. 4.5 Inequalities
  5. 4.6 Power Series
  6. 4.7 Derivatives and Differential Equations
  7. 4.8 Identities
  8. 4.9 Continued Fractions
  9. 4.10 Integrals
  10. 4.11 Sums
  11. 4.12 Generalized Logarithms and Exponentials
  12. 4.13 Lambert $W$-Function
• Trigonometric Functions
  1. 4.14 Definitions and Periodicity
  2. 4.15 Graphics
  3. 4.16 Elementary Properties
  4. 4.17 Special Values and Limits
  5. 4.18 Inequalities
  6. 4.19 Maclaurin Series and Laurent Series
  7. 4.20 Derivatives and Differential Equations
  8. 4.21 Identities
  9. 4.22 Infinite Products and Partial Fractions
  10. 4.23 Inverse Trigonometric Functions
  11. 4.24 Inverse Trigonometric Functions: Further Properties
  12. 4.25 Continued Fractions
  13. 4.26 Integrals
  14. 4.27 Sums

• Hyperbolic Functions
  1. 4.28 Definitions and Periodicity
  2. 4.29 Graphics
  3. 4.30 Elementary Properties
  4. 4.31 Special Values and Limits
  5. 4.32 Inequalities
  6. 4.33 Maclaurin Series and Laurent Series
  7. 4.34 Derivatives and Differential Equations
  8. 4.35 Identities
  9. 4.36 Infinite Products and Partial Fractions
  10. 4.37 Inverse Hyperbolic Functions
  11. 4.38 Inverse Hyperbolic Functions: Further Properties
  12. 4.39 Continued Fractions
  13. 4.40 Integrals
  14. 4.41 Sums
• Applications
  1. 4.42 Solution of Triangles
  2. 4.43 Cubic Equations
  3. 4.44 Other Applications
• Computation
  1. 4.45 Methods of Computation
  2. 4.46 Tables
  3. 4.47 Approximations
  4. 4.48 Software

3.12 Mathematical Constants4.1 Special Notation

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