Chapter 8 Incomplete Gamma and Related Functions

R. B. Paris Division of Mathematical Sciences, University of Abertay Dundee, Dundee, United Kingdom.

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Acknowledgements:

This chapter is based in part on Abramowitz and Stegun (1964, Chapters 5 and 6), by W. Gautschi and F. Cahill, and P. J. Davis, respectively.

Notes:

The main references used in writing this chapter are Erdélyi et al. (1953b), Luke (1969b), and Temme (1996b). For additional bibliographic reading see Gautschi (1998), Olver (1997b), and Wong (1989).

Referenced by:

§6.2(i), New Associate Editors for the DLMF, Profile Gergő Nemes, Profile Richard B. Paris, § ‣ Chapter Authors, § ‣ Associate Editors, § ‣ Associate Editors, Erratum (V1.0.5) for Chapters 8, 20, 36, § ‣ Software Cross Index

Permalink:

http://dlmf.nist.gov/8

   

• Notation
  1. 8.1 Special Notation
• Incomplete Gamma Functions
  1. 8.2 Definitions and Basic Properties
  2. 8.3 Graphics
  3. 8.4 Special Values
  4. 8.5 Confluent Hypergeometric Representations
  5. 8.6 Integral Representations
  6. 8.7 Series Expansions
  7. 8.8 Recurrence Relations and Derivatives
  8. 8.9 Continued Fractions
  9. 8.10 Inequalities
  10. 8.11 Asymptotic Approximations and Expansions
  11. 8.12 Uniform Asymptotic Expansions for Large Parameter
  12. 8.13 Zeros
  13. 8.14 Integrals
  14. 8.15 Sums
  15. 8.16 Generalizations

• Related Functions
  1. 8.17 Incomplete Beta Functions
  2. 8.18 Asymptotic Expansions of $I_x(a,b)$
  3. 8.19 Generalized Exponential Integral
  4. 8.20 Asymptotic Expansions of $E_p\left(z\right)$
  5. 8.21 Generalized Sine and Cosine Integrals
• Applications
  1. 8.22 Mathematical Applications
  2. 8.23 Statistical Applications
  3. 8.24 Physical Applications
• Computation
  1. 8.25 Methods of Computation
  2. 8.26 Tables
  3. 8.27 Approximations
  4. 8.28 Software

7.25 Software8.1 Special Notation

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