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

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

Foreword

Some 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 Tables

References

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

List of Volumes in the Mathematical Tables Series