LEADER 04114nam 2200601 450 001 9910827482503321 005 20230117095335.0 010 $a1-00-333959-X 010 $a1-003-33959-X 010 $a1-000-79559-4 010 $a87-7022-625-3 035 $a(CKB)4100000012160893 035 $a(MiAaPQ)EBC29002973 035 $a(Au-PeEL)EBL29002973 035 $a(OCoLC)1289259031 035 $a(MiAaPQ)EBC7078884 035 $a(Au-PeEL)EBL7078884 035 $a(EXLCZ)994100000012160893 100 $a20230117d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpecial functions and their application /$fBipin Singh Koranga, Sanjay Kumar Padaliya, and Vivek Kumar Nautiyal 205 $a1st ed. 210 1$aGistrup, Denmark ;$aLondon ;$aNew York, New York :$cRiver Publishers :$cRoutledge,$d[2021] 210 4$dİ2021 215 $a1 online resource (124 pages) 225 0 $aRiver Publishers series in mathematical and engineering sciences 311 $a87-7022-626-1 320 $aIncludes bibliographical references and index. 327 $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. 327 $a6.7 Associated Laguerre Polynomials -- 6.7.1 Properties of Associated Laguerre Polynomials -- 6.8 Exercises -- Bibliography -- Index -- About the Authors -- Back Cover. 330 $aThis short text gives clear descriptions and explanations of the Gamma function, the Probability Integral and its related functions, Spherical Harmonics Theory, The Bessel function, Hermite polynomials and Laguerre polynomials. 410 0$aRiver Publishers Series in Mathematical and Engineering Sciences. 606 $aFunctions, Special 606 $aFunctional analysis 606 $aGamma functions 615 0$aFunctions, Special. 615 0$aFunctional analysis. 615 0$aGamma functions. 676 $a515.5 700 $aKoranga$b Bipin Singh$01699108 702 $aPadaliya$b Sanjay Kumar 702 $aNautiyal$b Vivek Kumar 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827482503321 996 $aSpecial functions and their application$94117322 997 $aUNINA