Orders of Infinity, the Infinitärcalcül of Paul du Bois-Reymond (Classic Reprint)

Du Bois-R eymond sI nfinitarcalcul 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 caseD uB ois-R eymond was a mathematician of such power and originality that it would be a great pity if so much of his best work were allowed to be forgotten. There is, in Du Bois-R eymond soriginal memoirs, a good deal that would not be accepted as conclusive by modern analysts. He is also at times exceedingly obscure; his work would beyond doubt have attracted much more attention had it not been for the somewhat repugnant garb in which he was unfortunately wont to clothe his most valuable ideas. I have therefore attempted, in the following pages, to bring the I nfinitarcalcul up to date, stating explicitly and proving carefully a number of general theorems the truth of which Du BoisR eymond seems to have tacitly assumed I may instance in particular the theorem of in. 2. I have to thank Messrs J. E. Littlewood and G. N. Watson for their kindness in reading the proof-sheets, and Mr J. Jackson for the numerical results contained in Appendix III. G. H. H. TRINITY COLLEGE, A pril, 1910.
(Typographical errors above are due to OCR software and don't occur in the book.)

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