G. H. Hardy 
Orders of Infinity [PDF ebook] 
The 'Infinitarcalcul’ of Paul Orders Bois-Reymond

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. HE ideas of Du bois-reymond’s Infinitarcalcul are of great and growing importance in all branches of the theory of functions. With the particular system of notation that he invented, it is, no doubt, quite possible to dispense; but it can hardly be denied that the notation is exceedingly useful, being clear, concise, and expressive in a very high degree. In any case Du bois-reymond was a mathe matician of such power and originality that it would be a great pity if so much of his best work were allowed to be forgotten.