Special functions and their application / / Bipin Singh Koranga, Sanjay Kumar Padaliya, and Vivek Kumar Nautiyal

• Autore: Koranga Bipin Singh
• Pubblicazione: Gistrup, Denmark ; ; London ; ; New York, New York : , : River Publishers : , : Routledge, , [2021]; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (124 pages)
• Disciplina: 515.5
• Soggetto topico: Functions, Special; Functional analysis; Gamma functions
• Persona (resp. second.): PadaliyaSanjay Kumar; NautiyalVivek Kumar
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Special functions and their application
• ISBN: 1-00-333959-X; 1-003-33959-X; 1-000-79559-4; 87-7022-625-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910827482503321
• Lo trovi qui: Univ. Federico II
• Serie: River Publishers Series in Mathematical and Engineering Sciences.