H25B FLT DISPATCHED WITHOUT REQUIRED SPECIAL FLT PERMIT. LOGBOOK IMPROPERLY COMPLETED.

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WE HAD A FUEL BOOST PUMP FAILURE DURING A FLT TO BANGOR INTL; ME. AFTER LNDG; WE RPTED THE PROB TO OUR DISPATCH OFFICE. WE ALSO HAD AN A&P MECH WITH US ON THE ACFT. WE FOLLOWED THE MEL SECTION OF OUR FLT MANUAL FOR AN INOP FUEL BOOST PUMP. ALL OPERATOR (PLT) ACTIONS WERE TAKEN FOR THE SUBSEQUENT FLT FROM BANGOR TO OKC. THE A&P SIGNED OFF THE ACFT FORMS WITH THE MEL RELIEF. AFTER THE FLT; WE FOUND THAT SECTION II OF OUR OPS MANUAL (LIMITATIONS) SAYS THAT TKOF WITH 1 FUEL TANK BOOST PUMP INOP REQUIRES A 'SPECIAL FLT PERMIT.' AS FAR AS WE KNOW; WE DID NOT HAVE A SPECIAL FLT PERMIT; ONLY MEL RELIEF. THE MEL SECTION DOES NOT DIRECT YOU TO THIS SECTION. NEITHER OUR DISPATCH; OUR MECH NOR SYS MAINT PERSONNEL CAUGHT THIS ERROR. SUPPLEMENTAL INFO FROM ACN 574209: I ASSUMED ALL THE PROCS WERE COMPLETE. LATER I FOUND OUT THAT THE MECH DID NOT SIGN OFF THE OPS PROC IN THE 'CORRECTIVE ACTION BLOCK' EITHER. ALL OP PROCS WERE COMPLETED; JUST NOT SIGNED OFF IN ACFT FORMS. NEITHER OUR DISPATCH; OUR MECH OR SYS MAINT PERSONNEL CAUGHT THIS ERROR. NO SAFETY OF FLT ITEMS WERE VIOLATED.