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1、1ApplicationofWiener-HopftechniquetolinearnonhomogeneousintegralequationsforanewrepresentationofChandrasekhar’sH-functioninRadiativeTransfer,itsexistenceanduniqueness.RabindraNathDas*VisitingFacultyMember,HeritageInstituteofTechnology,ChowbagaRoad,Anandapur,P.O.EastKolkataTownship
2、,Kolkata-7000107,WestBengal,IndiaEmailaddress:rndas1946@yahoo.comAbstract:Inthispaper,thelinearnonhomogeneousintegralequationofH–functionsisconsideredtofindanewformofH-functionasitssolution.TheWiener–Hopftechniqueisusedtoexpressaknownfunctionintotwofunctionswithdifferentzonesofana
3、lyticity.Thelinearnonhomogeneousintegralequationisthereafterexpressedintotwodifferentsetsoffunctionshavingthedifferentzonesofregularity.ThemodifiedformofLiouville’stheoremisthereafterused,Cauchy’sIntegralformulaeareusedtodeterminefunctionalrepresentationoverthecutregioninacomplexp
4、lane.ThenewformofH-functionisderivedbothforconservativeandnon-conservativecases.Theexistenceofsolutionoflinearnonhomogeneousintegralequationsanditsuniquenessareshown.FornumericalcalculationofthisnewH-function,asetofusefulformulaearederivedbothforconservativeandnon-conservativecase
5、s.Keywords:Radiativetransfer,linearnonhomogeneousIntegralequations,Wiener-Hopftechnique,CauchyIntegralformulae.*Permanenetaddress:KB-9,Flat-7,Sector–3,SaltbLakecity(Bidhannagar),Kolkata–7000982Introduction:Theequationoftransferwhichgovernstheradiationfieldinamediumisanintegro-diff
6、erentialequationfortheintensityofradiation.Mostoftheproblemsinradiationtransportareessentiallythatofsolvingthatequationoftransfer.Theemergentintensityfromtheboundingfaceandintensityofradiationatanyopticaldepthoftheplane-parallelhomogeneousscatteringsemi-infiniteatmospherearefoundi
7、ntermsofH–functionsofChandrasekhar[1].Incasesofdiffusereflectionandtransmissionfromtheboundingfacesinahomogeneousplaneparallelatmosphereoffinitethickness,Chandrasekhar[1]obtainedsolutionsintermsofcoupledX-Yfunctions.Chandrashekhar[1],Mullikin[2]andDas[3]showedthatthoseX-Yfunctions
8、canbeexpressedintermsofH-function
