Results of Elliptic Integrals

Notation

19.1 Special Notation

Legendre’s Integrals

19.2 Definitions
19.3 Graphics
19.4 Derivatives and Differential Equations
19.5 Maclaurin and Related Expansions
19.6 Special Cases
19.7 Connection Formulas
19.8 Quadratic Transformations
19.9 Inequalities
19.10 Relations to Other Functions
19.11 Addition Theorems
19.12 Asymptotic Approximations
19.13 Integrals of Elliptic Integrals
19.14 Reduction of General Elliptic Integrals

Symmetric Integrals

19.15 Advantages of Symmetry
19.16 Definitions
19.17 Graphics
19.18 Derivatives and Differential Equations
19.19 Taylor and Related Series
19.20 Special Cases
19.21 Connection Formulas
19.22 Quadratic Transformations
19.23 Integral Representations
19.24 Inequalities
19.25 Relations to Other Functions
19.26 Addition Theorems
19.27 Asymptotic Approximations and Expansions
19.28 Integrals of Elliptic Integrals
19.29 Reduction of General Elliptic Integrals

Applications

19.30 Lengths of Plane Curves
19.31 Probability Distributions
19.32 Conformal Map onto a Rectangle
19.33 Triaxial Ellipsoids
19.34 Mutual Inductance of Coaxial Circles
19.35 Other Applications

Computation

19.36 Methods of Computation
19.37 Tables
19.38 Approximations
19.39 Software