Front Cover; Theory and Application of Special Functions; Copyright Page; Table of Contents; Foreword; Preface; Chapter 1. Computational Methods in Special Functions-A Survey; Introduction; 1. Methods based on preliminary approximation; 2. Methods based on linear recurrence relations; 3. Nonlinear recurrence algorithms for elliptic integrals and elliptic functions; 4. Computer software for special functions; REFERENCES; Chapter 2. Unsolved Problems in the Asymptotic Estimation of Special Functions; Abstract; 1. INTRODUCTION; PART I. THE TOOLS OF ASYMPTOTIC ANALYSIS; 2. INTEGRALS

3. SUMS AND SEQUENCES4. LINEAR ORDINARY DIFFERENTIAL EQUATIONS; PART II. ASYMPTOTIC ESTIMATES OF THE SPECIAL FUNCTIONS; 5. FUNCTIONS OF ONE OR TWO VARIABLES; 6. FUNCTIONS OF THREE VARIABLES; 7. FUNCTIONS OF FOUR OR MORE VARIABLES; ACKNOWLEDGMENTS; REFERENCES; Chapter 3. Periodic Bernoulli Numbers, Summation Formulas and Applications; 1. Introduction.; 2. Periodic Bernoulli numbers and polynomials; 3. The periodic Poisson and periodic Euler-Maclaurin summation; 4. The distribution of quadratic residues; 5. Power sums and cotangent sums; 6. Gauss sums; 7. Functional equations

8. A trigonometric series of Hardy and Littlewood9. Infinite series of ordinary Bessel functions; 10. Infinite series of modified Bessel functions; 11. Entries from Ramanujan's Notebooks and kindred formulae; REFERENCES; Chapter 4. Problems and Prospects for Basic Hypergeometric Functions; 1. Introduction; 2. Partitions identities; 3. Identities for Multiple Hypergeometric Series; 4. Basic Appell and Lauricella Series; 5. MacMahon's Master Theorem and the Dyson Conjecture; 6. Saalschützian Series and Inversion Theorems; 7. Conclusion.; REFERENCES

Chapter 5. An Introduction to Association Schemes and Coding TheoryABSTRACT; 1 INTRODUCTION; 2 Error-Correcting Codes; 3 Association Schemes; 4 The Hamming Association Scheme; 5 The Johnson Association Scheme; 6 Association Schemes Obtained from Graphs and Other Sources; 7 The Linear Programming Bound; 8 Properties of Perfect Codes; REFERENCES; Chapter 6. Linear Growth Models with Many Types and Multidimensional Hahn Polynomials; 1. Multi-allele Moran mutation models; 2. Representation of P(t).; 3. Relation with multi-dimensional linear growth; 4. The case r = 2 and the Hahn polynomials

5. Moran model with r types.6. Linear growth model with r types; 7. The eigenfunctions when; REFERENCES; Chapter 7. Orthogonal Polynomials Revisited; I. Introduction; II. Polynomials on the Real Axis; III. Applications; IV. Polynomials on the Unit Circle; V. Conclusion; FOOTNOTES; Chapter 8. Symmetry, Separation of Variables, and Special Functions; REFERENCES; Chapter 9. Nicholson-Type Integrals for Products of Gegenbauer Functions and Related Topics; ABSTRACT; 1. INTRODUCTION; 2. DERIVATION OF A NICHOLSON-TYPE FORMULA FOR GEGENBAUER FUNCTIONS; 3. SOME APPLICATIONS FOR GEGENBAUER FUNCTIONS