Theorie der Modular-Functionen und der Modular-Integrale.

Berlin, G. Reimer, 1840. 4to. In "Journal für die reine und angewandte Mathematik, 1840, 3 Heft". Without backstrip. Fine and clean. [Guderman:] Pp. 240-292. First printing of the second part of Gudermann's papers on modular functions and modular integrals, ideas which anticipated his 1844-book."Gudermann devoted much more attention to the theory of special functions. After the earlier works of Leonhard Euler, John Landen, and A. M. Legendre (Gauss's results were still in manuscript), Niels Abel's studies on elliptical functions, published mostly in A. L. Crelle's Journal für reine und angewandte Mathematik, represented an important divide in treating this area. In 1829 Carl Jacobi's book Fundamenta nova theoriae functionum ellipticarum was published. At the time Gudermann was one of the first mathematicians to expand on these results. Beginning with volume 6 (1830) of Crelle's Journal, he published a series of papers which he later summarized in two books: Theorie der Potenzialoder cyklisch-hyperbolischen Functionen (1833) and Theorie der Modular-Functionen und der Modular-Integrale (1844), which were to have had a sequel which was never written." (DSB).…