Results of Incomplete Gamma and Related Functions

Notation

8.1 Special Notation

Incomplete Gamma Functions

8.2 Definitions and Basic Properties
8.3 Graphics
8.4 Special Values
8.5 Confluent Hypergeometric Representations
8.6 Integral Representations
8.7 Series Expansions
8.8 Recurrence Relations and Derivatives
8.9 Continued Fractions
8.10 Inequalities
8.11 Asymptotic Approximations and Expansions
8.12 Uniform Asymptotic Expansions for Large Parameter
8.13 Zeros
8.14 Integrals
8.15 Sums
8.16 Generalizations

Related Functions

8.17 Incomplete Beta Functions
8.18 Asymptotic Expansions of ${\displaystyle{\displaystyle I_{x}\left(a,b\right)}}$
8.19 Generalized Exponential Integral
8.20 Asymptotic Expansions of ${\displaystyle{\displaystyle E_{p}\left(z\right)}}$
8.21 Generalized Sine and Cosine Integrals

Applications

8.22 Mathematical Applications
8.23 Statistical Applications
8.24 Physical Applications

Computation

8.25 Methods of Computation
8.26 Tables
8.27 Approximations
8.28 Software