数学专业英语作业.doc

原文:AChild’,?Mostreaderswillnothaveencounteredaderivativeof“order”before,’Hospital,Euler,Lagrange,Laplace,Riemann,Fourier,Liouville,“fractionalcalculus.”Twotextbooksonthesubjectatthegraduatelevelhaveappearedrecently,[9]and[11].Also,twocollectionsofpapersdeliveredatconferencesarefoundin[7]and[14].AsetofveryreadableseminarnoteshasbeenpreparedbyWheeler[15],—lemma—theoremapproach,weexploretheideaofafractionalderivativebyfirstlookingatexamplesoffamiliarnthorderderivativeslikeandthenreplacingthenaturalnumbernbyothernumberslikeInthisway,likedetectives,.(ForaquicklookatformaldefinitionsseetheexcellentexpositorypaperbyMiller[8].)Astheexplorationcontinues,?Letussee.....,and,ingeneral,?plexnumberlike1+i?Wewillbeboldandwrite(1)foranyvalueof,integer,rational,irrational,(1)whenisa