الفهرس | Only 14 pages are availabe for public view |
Abstract This thesisaimstointroduceamethodforobtainingindefinite q-integrals involvingsome q-specialfunctionsthatsatisfyhomogeneous(nonhomogeneous) self-adjointsecond-order q-difference equations.Many q-integrals,bothprevi- ously knownandcompletelynew,arederivedusingthemethod,andwerefor- mulatethemethodintermsof q-Riccati equations,whicharenonlinearand first-order. Wederive q-integralsusingfragmentsoftheseRiccatiequations, and hereonlytwospecificfragmenttypesareexaminedindetail.Thenwe use Heinecontiguousrelationsforthebasichypergeometricfunction 2_1, the q-integratingfactormethodforsolvinglinearfirst-order q-difference equations, and anindefinite q-integralformulainvolvingtwoarbitraryfunctionstoderive indefinite q-integralsinvolvingquotientsofthehyper-geometricfunctions 2_1. |