LEADER 03970nam 2200685Ia 450 001 9910438146203321 005 20251116201910.0 010 $a9781299335691 010 $a1299335691 010 $a9783034805636 010 $a3034805632 024 7 $a10.1007/978-3-0348-0563-6 035 $a(CKB)2670000000337135 035 $a(EBL)1082180 035 $a(OCoLC)828794622 035 $a(SSID)ssj0000870779 035 $a(PQKBManifestationID)11523248 035 $a(PQKBTitleCode)TC0000870779 035 $a(PQKBWorkID)10819306 035 $a(PQKB)10620113 035 $a(DE-He213)978-3-0348-0563-6 035 $a(MiAaPQ)EBC1082180 035 $a(PPN)168307464 035 $a(MiFhGG)9783034805636 035 $a(EXLCZ)992670000000337135 100 $a20130217d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpecial functions of mathematical (geo-)physics /$fWilli Freeden, Martin Gutting 205 $a1st ed. 2013. 210 $aBasel $cSpringer$d2013 215 $a1 online resource (504 p.) 225 1 $aApplied and numerical harmonic analysis 300 $aDescription based upon print version of record. 311 08$a9783034807746 311 08$a3034807740 311 08$a9783034805629 311 08$a3034805624 320 $aIncludes bibliographical references and index. 327 $a1 Introduction: Geomathematical Motivation -- Part I: Auxiliary Functions -- 2 The Gamma Function -- 3 Orthogonal Polynomials -- Part II: Spherically Oriented Functions.- 4 Scalar Spherical Harmonics in R^3 -- 5 Vectorial Spherical Harmonics in R^3 -- 6 Spherical Harmonics in R^q -- 7 Classical Bessel Functions -- 8 Bessel Functions in R^q -- Part III: Periodically Oriented Functions -- 9 Lattice Functions in R -- 10 Lattice Functions in R^q -- 11 Concluding Remarks -- References -- Index. 330 $aSpecial functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises. 410 0$aApplied and numerical harmonic analysis. 606 $aGeodynamics$xMathematics 606 $aFunctions, Special 615 0$aGeodynamics$xMathematics. 615 0$aFunctions, Special. 676 $a516.83 676 $a550.151 700 $aFreeden$b W$g(Willi)$01074834 701 $aGutting$b Martin$01755300 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438146203321 996 $aSpecial functions of mathematical (geo-)physics$94468603 997 $aUNINA