Tables and Formulae for the Spherical Functions Pm – ½ + i t (Z)

ForewordSome Properties of the Functions Pm-1/2+iτ(z) 1. Introduction 2. Definition of the Spherical Functions 3. Representation of the Functions Pm-1/2+iτ(z) by Hypergeometric Series 4. Integral Representations 5. Functional Relationships 6. Expansions in Series of Powers of τ 7. Asymptotic Representations for Large Values of τ 8. Properties of the Zeros of the Spherical Functions 9. Behaviour of the Functions Pm-1/2+iτ(z) in the Neighbourhood of Singular Points 10. Addition Formulae 11. Expansion of an Arbitrary Function in a Series of Functions Pm-1/2+iτ(cosh η) 12. Representation of an Arbitrary Function as an Integral Involving the Functions Pm-1/2+iτ(cosh η) 13. Functions of the Second Kind 14. Examples of the Use of the Functions Pm-1/2+iτ(z) in Problems of Mathematical Physics Description of the TablesReferencesTable 1Table 2Table 3Table 4Table 5Table 6Table 7Table 8List of Volumes in the Mathematical Tables Series