Results of Confluent Hypergeometric Functions

Notation

13.1 Special Notation

Kummer Functions

13.2 Definitions and Basic Properties
13.3 Recurrence Relations and Derivatives
13.4 Integral Representations
13.5 Continued Fractions
13.6 Relations to Other Functions
13.7 Asymptotic Expansions for Large Argument
13.8 Asymptotic Approximations for Large Parameters
13.9 Zeros
13.10 Integrals
13.11 Series
13.12 Products
13.13 Addition and Multiplication Theorems

Whittaker Functions

13.14 Definitions and Basic Properties
13.15 Recurrence Relations and Derivatives
13.16 Integral Representations
13.17 Continued Fractions
13.18 Relations to Other Functions
13.19 Asymptotic Expansions for Large Argument
13.20 Uniform Asymptotic Approximations for Large Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu}
13.21 Uniform Asymptotic Approximations for Large Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa}
13.22 Zeros
13.23 Integrals
13.24 Series
13.25 Products
13.26 Addition and Multiplication Theorems

Applications

13.27 Mathematical Applications
13.28 Physical Applications

Computation

13.29 Methods of Computation
13.30 Tables
13.31 Approximations
13.32 Software