Results of Legendre and Related Functions

Notation

14.1 Special Notation

Real Arguments

14.2 Differential Equations
14.3 Definitions and Hypergeometric Representations
14.4 Graphics
14.5 Special Values
14.6 Integer Order
14.7 Integer Degree and Order
14.8 Behavior at Singularities
14.9 Connection Formulas
14.10 Recurrence Relations and Derivatives
14.11 Derivatives with Respect to Degree or Order
14.12 Integral Representations
14.13 Trigonometric Expansions
14.14 Continued Fractions
14.15 Uniform Asymptotic Approximations
14.16 Zeros
14.17 Integrals
14.18 Sums
14.19 Toroidal (or Ring) Functions
14.20 Conical (or Mehler) Functions

Complex Arguments

14.21 Definitions and Basic Properties
14.22 Graphics
14.23 Values on the Cut
14.24 Analytic Continuation
14.25 Integral Representations
14.26 Uniform Asymptotic Expansions
14.27 Zeros
14.28 Sums
14.29 Generalizations

Applications

14.30 Spherical and Spheroidal Harmonics
14.31 Other Applications

Computation

14.32 Methods of Computation
14.33 Tables
14.34 Software