04114nam 2200601 450 991079462060332120230117095335.01-00-333959-X1-003-33959-X1-000-79559-487-7022-625-3(CKB)4100000012160893(MiAaPQ)EBC29002973(Au-PeEL)EBL29002973(OCoLC)1289259031(MiAaPQ)EBC7078884(Au-PeEL)EBL7078884(EXLCZ)99410000001216089320230117d2021 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierSpecial functions and their application /Bipin Singh Koranga, Sanjay Kumar Padaliya, and Vivek Kumar Nautiyal1st ed.Gistrup, Denmark ;London ;New York, New York :River Publishers :Routledge,[2021]©20211 online resource (124 pages)River Publishers series in mathematical and engineering sciences87-7022-626-1 Includes bibliographical references and index.Front 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.6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover.This 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.River Publishers Series in Mathematical and Engineering Sciences.Functions, SpecialFunctional analysisGamma functionsFunctions, Special.Functional analysis.Gamma functions.515.5Koranga Bipin Singh1509249Padaliya Sanjay KumarNautiyal Vivek KumarMiAaPQMiAaPQMiAaPQBOOK9910794620603321Special functions and their application3811031UNINA