318 ON THE RECENT PROGRESS OF ANALYSIS. 



ten. C. xxvii. 185. M. Jacob! has criticised this paper (of 

 which a translation appears in Liouville's Journal, x. 44 5) in the 

 thirtieth volume of Ci\ lie's Journal. 



Elementare Ableitung einer merkwiirdiger Relation zwischen 



zwei unendlichen Producten. C. xxvii. 285. V. R. p. 293. 



Beitrage zur Theorie der Elliptischen Functionen. C. xxx. 



185, 211. This paper contains a demonstration of the funda- 

 mental formula of elliptic functions. Y. R. p. 295. 



GUDERMANN. Integralia Elliptica Tertise Speciei Reducendi Metho- 

 dus Simplicior, &c. C. xiv. 159, 185. V. R. p. 291. 



Einige Bemerkungen liber Elliptische Functionen. C. xvi. 78. 



Series novae quarum ope Integralia Elliptica Primse et Se- 



cundse Speciei computantur, &c. C. xvi. 366, and xvn. 382. 



Theorie der Modular Functionen und der Modular Integrale. 



C. xvm. 1, 142, 220, 303; xix. 46, 119, 244; xx. 62, 103; 

 XXL 240 ; xxni. 301 ; xxv. 281. A systematic treatise on 

 elliptic functions. V. R. p. 291. 



GUTZLAFF. ^Equatio Modularis pro Transformation Functionum 



Ellipticarum Septimi Ordinis. C. xn. 173. Y. R. p. 291. 

 HAEDENKAMP. De Transformation Integralis 



I! 



nV - sin 2 </> cos 2 \js) ' 

 C. xx. 97. It is shown to be the product of two elliptic 

 integrals. 



Tiber Transformation vielfacher Integrale. C. xxii. 184. 



Analogous to the researches of M. Catalan in the * Memoires de 

 Bruxelles,' which appears to have been previously published. 



tJber Abelsche Integrale. C. xxv. 178. Y. R. p. 309. 



HERMITE. Sur la Theorie des Transcendantes a Difierentielles Al- 

 gebriques. L. ix. 353. Extracted from the Comptes Rendus ' 

 [June 1844]. This note, which contains scarcely more than an 

 indication of M. Hermite's results, may be said to mark the 

 furthest advance yet made in the theory of the comparison of 

 transcendents. Y. R. p. 312. 



HILL. Exemplum usus Functionum Iteratarum, <fec. C. xi. 193. 

 This paper contains some interesting applications of the calculus 

 of functions to the comparison of transcendents. Y. R. p. 250. 



JACOBI. Addition au Memoire de M. Abel sur les Fonctions Ellip- 

 tiques. C. in. 86. A short note, containing an important 

 simplification of Abel's method of solving the equation of the 

 problem of division. Y. R. p. 277. 



Note sur la Decomposition d'un Nombre donne* en quatre 



