LEADER 05008nam 2200613 450 001 9910786639303321 005 20230120014631.0 010 $a1-4832-1616-0 035 $a(CKB)3710000000200376 035 $a(EBL)1901405 035 $a(SSID)ssj0001267405 035 $a(PQKBManifestationID)12485382 035 $a(PQKBTitleCode)TC0001267405 035 $a(PQKBWorkID)11263650 035 $a(PQKB)11089873 035 $a(MiAaPQ)EBC1901405 035 $a(EXLCZ)993710000000200376 100 $a20150120h19751975 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTheory and application of special functions $eproceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2, 1975 /$fedited by Richard A. Askey 210 1$aNew York, New York ;$aLondon, England :$cAcademic Press,$d1975. 210 4$dİ1975 215 $a1 online resource (573 p.) 225 1 $aMathematics Research Center, the University of Wisconsin ;$vPublication no. 35 300 $aDescription based upon print version of record. 311 $a1-322-55721-7 311 $a0-12-064850-4 320 $aIncludes bibliographical references and index. 327 $aFront 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 327 $a3. 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 327 $a8. 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. Saalschu?tzian Series and Inversion Theorems; 7. Conclusion.; REFERENCES 327 $aChapter 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 327 $a5. 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 327 $a4. DEDUCTIONS FOR OTHER FUNCTIONS 330 $aTheory and Application of Special Functions 410 0$aPublication ... of the Mathematics Research Center, the University of Wisconsin ;$vPublication no. 35. 606 $aFunctions, Special$vCongresses 615 0$aFunctions, Special 676 $a510/.8 s 676 $a515/.5 702 $aAskey$b Richard A. 712 02$aUniversity of Wisconsin--Madison.$bMathematics Research Center. 712 12$aAdvanced Seminar on Special Functions 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910786639303321 996 $aTheory and application of special functions$9349045 997 $aUNINA