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...Summable trigonometric series r d james l introduction one of the problems in theory trigono metric form od zyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba an cos nx b sin n a is that suitably defining process integration such if converges to function f x then integrable and coefficients are given fourier problem has been nf solved by denjoy verblunsky marcinkiewicz zygmund burkill s paper burkil first additional hypotheses other than convergence were made all papers some modification formulas was necessary extension consider c k this wolf when sum func tion perron inte gration which may be applied any condition involving conjugate imposed with extra it proved formal product px or also o pa properties integrated discussed shown generalized pfc integral integrates satisfying addition natural these principal results they described briefly for special case author invited address at summer meeting american mathematical society possible improve slightly only require summability excepti...