footfootnoteforfor allfor all values offor all xfor completenessfor iffor instancefor our purposefor performingfor somefor sufficiently large valuesfor the casefor the reasonfor the sake offor this reasonfor typographical reasonsfor wheneverfor whichforbiddenforceforce polygonforcedforced ocillatory motionforced oscillationforced oscillationsforced vibrationforced vibrationsforecastforegoingforehand weldingforestforkformform of classformalformal certaintyformal definitionformal definition of probabilityformal expressionformal groupformal linear combinationformal logicformal methodformal organizationformal power seriesformal prerequisiteformal ruleformal statement