Theory and application of special functions : proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975 /

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Theory and Application of Special Functions.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores Corporativos: Advanced Seminar on Special Functions Madison, Wis., University of Wisconsin--Madison. Mathematics Research Center
Otros Autores: Askey, Richard
Formato: Electrónico Congresos, conferencias eBook
Idioma:Inglés
Publicado: New York : Academic Press, 1975.
Colección:Publication ... of the Mathematics Research Center, the University of Wisconsin--Madison ; no. 35.
Temas:
Functions, Special > Congresses.
Fonctions spéciales > Congrès.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Functions, Special
Spezielle Funktion
Kongreß.
Congress
proceedings (reports)
Conference papers and proceedings
Conference papers and proceedings.
Actes de congrès.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

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