‎"HERMITE, CHARLES (+) JACOBI.‎
‎Extraits de deux lettres de M. Charles Hermite a M. Jacobi. - [THE VERY FIRST RESEARCH BY HERMITE]‎

‎Berlin, G. Reimer, 1846. 4to. No wrappers. In ""Journal für die reine und angewandte Mathematik. Hrsg. von A.L. Crelle"", 32. Band, 1846"". Entire issue offered.‎

Reference : 47328

‎First appearance of these two fundamental letters, representing the very first research by Hermite, sent from Charles Hermite to Jacobi"" the letter first in January 1843, the second in august 1944. Hermite's first letter is on the extension of Abelian functions of the theorem given by Abel on the division of the argument of elliptic functions and begins as follows: ""The study of your memoir published in Crelle's journal under the title 'De functionibus quadruliciter periodicis quibus theoria transcendentium Abelianarum innititur' has led me, for the division of the argument in these functions to a theorem analogous to that which you have given in the third volume of that journal for obtaining the simplest expression of the roots of the equation treated by Abel"". Hermite shows that the corresponding equations are soluble by radicals and he treats of the reduction of the equation in the case of the division of complete functions. Hermite's second letter gives the proof of the formula for the transformation of elliptic functions which Jacobi had given without proof six years before. ""These two letters, embodying as they do the first original researches of Hermite, were given by Jacobi the same cordial reception as had been accorded to his first letter of 1827 by Legendre. Writing on the 24th June, 1843, in reply to Hermite's first letter, Jacobi says ""I thank you very sincerely for the beautiful and important communication which you have made to me about the division of Abelian functions. You have opened, by the discovery of this division, a vast field of researches and new discoveries which will give a great impetus to the analytical art."" (Prasad, Some Great Mathematicians of the Nineteenth Century).‎