简介：ThispapergivesthetheoremsconcerningthesummationoftrigonometricseriesWiththehelpofFouriertransforms.BymeansoftheknownresultsofFouriertransforms,manydifficultandcomplexproblemsofsummationoftrigonometricseriescanbesolved.Thismethodisacomparativelyunusualwaytofindthesummationoftrigonometricseries.andhasbeenusedtoestablishthecomprehensivetableofsummationoftrigonometricseries.Inthistable.10thousandseriesaregiven.andmostofthemarenew.

简介：Inthispaper,thetheoremsconcerningthesummationofFourierserieswithparameteraregivenbyusingtheLaplacetransforms.BymeansoftheknownresultofLaplacetransforms,manynew,importantproblemsofsummationofFourierserieswithparameterinmechanicscanbesolved.

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简介：Theboundaryvalueproblemofplatebendingproblemontwo-parameterfoundationwasdiscussed.Usingtwoseriesofthehigh-orderfundamentalsolutionsequences,namely,thefundamentalsolutionsequencesforthemulti-harmonicoperatorandLaplaceoperator,applyingthemultiplereciprocitymethod(MRM),theMRMboundaryintegralequationforplatebendingproblemwasconstructed.ItprovesthattheboundaryintegralequationderivedfromMRMisessentiallyidenticaltotheconventionalboundaryintegralequation.HencetheconvergenceanalysisofMRMforplatebendingproblemcanbeobtainedbytheerrorestimationfortheconventionalboundaryintegralequation.Inaddition,thismethodcanextendtothecaseofmoreseriesofthehigh-orderfundamentalsolutionsequences.