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001			EBC29002973
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005			20240724115758.0
006			m o d |
007			cr cnu||||||||
008			240724s2021 xx o ||||0 eng d
020			_a9788770226257 _q(electronic bk.)
020			_z9788770226264
035			_a(MiAaPQ)EBC29002973
035			_a(Au-PeEL)EBL29002973
035			_a(OCoLC)1289259031
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA351
082	0		_a515.5
100	1		_aKoranga, Bipin Singh.
245	1	0	_aSpecial Functions and Their Application.
250			_a1st ed.
264		1	_aAalborg : _bRiver Publishers, _c2021.
264		4	_c©2021.
300			_a1 online resource (124 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
505	0		_aFront Cover -- Special Functions and their Applications -- Contents -- Preface -- List of Tables -- 1 The Gamma Function -- 1.1 Definition of Gamma Function -- 1.2 Gamma Function and Some Relations -- 1.3 The Logarithmic Derivative of the Gamma Function -- 1.4 Asymptotic Representation of the Gamma Function for Large |z| -- 1.5 Definite Integrals Related to the Gamma Function -- 1.6 Exercises -- 2 The Probability Integral and Related Functions -- 2.1 The Probability Integral and its Basic Properties -- 2.2 Asymptotic Representation of Probability Integral for Large |z| -- 2.3 The Probability Integral of Imaginary Argument -- 2.4 The Probability Fresnel Integrals -- 2.5 Application to Probability Theory -- 2.6 Application to the Theory of Heat Conduction -- 2.7 Application to the Theory of Vibrations -- 2.8 Exercises -- 3 Spherical Harmonics Theory -- 3.1 Introduction -- 3.2 The Hypergeometric Equation and its Series Solution -- 3.3 Legendre Functions -- 3.4 Integral Representations of the Legendre Functions -- 3.5 Some Relations Satisfied by the Legendre Functions -- 3.6 Workskian of Pairs of Solutions of Legendre's Equation -- 3.7 Recurrence Relations for the Legendre Functions -- 3.8 Associated Legendre Functions -- 3.9 Exercises -- 4 Bessel Function -- 4.1 Bessel Functions -- 4.2 Generating Function -- 4.3 Recurrence Relations -- 4.4 Orthonormality -- 4.5 Application to the Optical Fiber -- 4.6 Exercises -- 5 Hermite Polynomials -- 5.1 Hermite Functions -- 5.2 Generating Function -- 5.3 Recurrence Relations -- 5.4 Rodrigues Formula -- 5.5 Orthogonality and Normalilty -- 5.6 Application to the Simple Harmonic Oscillator -- 5.7 Exercises -- 6 Laguerre Polynomials -- 6.1 Laguerre Functions -- 6.2 Generating Function -- 6.3 Recurrence Relations -- 6.4 Rodrigues Formula -- 6.5 Orthonormality -- 6.6 Application to the Hydrogen Atom.
505	8		_a6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover.
520			_aThis short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials.
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.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aKoranga, Bipin Singh _tSpecial Functions and Their Application _dAalborg : River Publishers,c2021 _z9788770226264
797	2		_aProQuest (Firm)
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=29002973 _zClick to View
999			_c34092 _d34092