000			06216nam a22004453i 4500
001			EBC1901405
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005			20240729123318.0
006			m o d |
007			cr cnu||||||||
008			240724s1975 xx o ||||0 eng d
020			_a9781483216164 _q(electronic bk.)
020			_z9780120648504
035			_a(MiAaPQ)EBC1901405
035			_a(Au-PeEL)EBL1901405
035			_a(CaPaEBR)ebr11003779
035			_a(CaONFJC)MIL687003
035			_a(OCoLC)898771916
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA3.T446 1975eb
100	1		_aAskey, Richard.
245	1	0	_aTheory and Application of Special Functions : _bProceedings of an Advanced Seminar Sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31-April 2 1975.
250			_a1st ed.
264		1	_aSan Diego : _bElsevier Science & Technology, _c1975.
264		4	_c©1975.
300			_a1 online resource (573 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_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 -- 3. SUMS AND SEQUENCES -- 4. 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 Littlewood -- 9. 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.
505	8		_aChapter 5. An Introduction to Association Schemes and Coding Theory -- ABSTRACT -- 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 -- 4. DEDUCTIONS FOR OTHER FUNCTIONS -- 5. CONCLUSIONS -- FOOTNOTES -- REFERENCES -- Chapter 10. Positivity and Special Functions -- 1. Introduction -- 2. Background material. -- 3. Computation. -- 4. Recurrence relations. -- 5. Maximum principles. -- 6. Estimation. -- 7. Absolutely monotonie and completely monotonie functions -- 8. Sums of squares. -- 9. Additional comments. -- REFERENCES -- Chapter 11. Two-Variable Analogues of the Classical Orthogonal Polynomials -- 1. Introduction -- 2. Jacobi polynomials -- 3. Methods of constructing two-variable analogues of the Jacobipolynomials.
505	8		_a4. Differential recurrence relations and other analytic properties -- 5. Orthogonal polynomials in two variables as spherical functions -- REFERENCES -- Chapter 12. Special Functions of Matrix and Single Argument in Statistics -- FOREWORD -- INTRODUCTION -- I. Zonal Polynomials of the Real Positive Definite Symmetric Matrices -- II. Orthogonal Polynomials of Matrix Argument -- III. Differential Equations for Hypergeometric Functions of Matrix Argument -- IV. Probability Functions of Ordered Roots -- REFERENCES -- Chapter 13. Some Properties of Determinants of Orthogonal Polynomials -- Introduction -- 1. Recurrence formulas -- 2. CHRISTQFFEL-DAJRBOUX FORMULA AND WRONSKIAN IDENTITIES. -- 3. Further Properties -- REFERENCES -- Index.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aFunctions, Special -- Congresses.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aAskey, Richard _tTheory and Application of Special Functions _dSan Diego : Elsevier Science & Technology,c1975 _z9780120648504
797	2		_aProQuest (Firm)
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=1901405 _zClick to View
999			_c45190 _d45190