4040 



Elliptic Integrals 



4040 



of 1st kind, infinitely many normal forms. 



Klein, C. F. Munch. Ak. Sb. 10 (1880) 533-. 

 , interpretation, geometric. Mansion, 



. Brux. S. Sc. A. 13 (1889) (Pt. 1) 47-. 

 , inversion. Kluyver, J. C. N. Arch. 



Wisk. 4 (1899) 109- ; Fschr. Mth. (1899) 400. 

 , new transcendental transforming into 



a circular function. laggi, E. N. A. Mth. 



19 (1900) 537-. 

 , normal forms of 3rd and 5th degree. 



Bianchi, L. Mth. A. 17 (1880) 234-. 

 , representation , geometric . Morgan, A . 



Edinb. Mth. S. P. 15 (1897) 2-. 



, transformation of integrals of 

 irrational differentials to normal form. 

 Steen, A. Kjob. Skr. 8 (1870) 183-. 



and 2nd kinds, differential equations 

 satisfied by moduli. Fuchs, L. Crelle J. 

 Mth. 112 (1893) 156-. 



, series for calculating, etc. 

 Gudermann, C. Crelle J. 16 (1837) 366-; 

 17 (1837) 382-. 



, 2nd and 3rd kinds, solution of 



by. Simony, 0. Arch. Mth. Ps. 55 (1873) 193-. 



2nd kind. Thomae, C. J. Crelle J. Mth. 

 93 (1882) 69-; 94 (1883) 241- ; Z. Mth. Ps. 

 27 (1882) 179-. 



, functions inverse to. Glaisher, 

 J. W. L. Camb. Ph. S. P. 5 (1886) 372-. 



, representation, mechanical. Darwin, 



G. H. Mess. Mth. 4 (1875) 113-. 



and 3rd kinds, expression by functions. 



Pokorny, M. Z. Mth. Ps. 10 (1865) 317-. 



3rd kind. Newman, F. W. Camb. and 

 Dubl. Mth. J. 8 (1853) 190-. 



. Hermite, C. C. E. 94 (1882) 901-. 



. Kummell, C. H. A. Mth. 2 (1885- 



86) 73-, 104-. 

 . Weyr, E. [1891] Prag Ceske Ak. 



Fr. Jos. Ez. (Tfida 2) 1 (1892) Art. 6, 9 pp. 

 . Mansion, . Brux. S. Sc. A. 



21 (1897) (Pt. 1) 15-. 

 , formula. Cayley, A. L. Mth. S. P. 



13 (1882) 175-. 



, formulae, complementary moduli. 

 Salvert, F. de. C. E. 120 (1895) 1208-. 



, reducible to 1st kind. Saalschiitz , L. 



Z. Mth. Ps. 34 (1889) 199-. 

 , reduction. Gudermann, C. Crelle 



J. 14 (1835) 169-, 185-. 

 linear transformation. Burnside, W. Mess. 



Mth. 21 (1892) 170-. 

 of 1st and 2nd order, relation between. Childe, 



(Rev.) G. F. Mess. Mth. 19 (1890) 155-. 

 periods. Bruns, H. Mth. A. 27 (1886) 234-. 

 . Jamet, V. N. A. Mth. 10 (1891) 193-. 

 and polynomials of 4th degree. Tannenberg, 



W. de. Bordeaux S. Sc. Mm. 3 (1899) 277-. 

 properties, geometric. Booth, J. Phil. Trans. 



(1852) 311- ; (1854) 53-. 

 in real form, reduction. Scheibner, W. 



[1879-80] Leip. Mth. Ps. Ab. 12 (1883) 



57-, i . 

 reduction. Genocchi, A. [1864] A. Mt. 6 



(1864) 5-; Tor. Lav. Sc. Fis. Mt. (1869) 39-. 



reduction. Kluyver, J. C. C. B. 116 (1893) 48-. 



to. Aronhold, S. H. Berl. Mb. (1861) 

 462-. 



canonical form. Heine, H. E. [1855] 



Crelle J. 53 (1857) 199-. 



of definite integrals to. Lindman, C. F. 

 Stockh. Ofv. 36 (1879) No. 6, 9-. 



integral, containing square root of quartic, 



and calculation of modulus. Alexeeff, N. 

 C. B. 59 (1864) 244-. 



to Jacobi's functions. Green-hill t A. G. 

 QJ. Mth. 18 (1882) 66-. 



normal form. Vorsteher, E. Z. Mth. 



Ps. 32 (1887) 145-. 

 . Stieltjes, T. J. C. E. 107 (1888) 



651-. 

 relating to continued fractions. Steen, A. (xn) 



Ts. Mth. 3 (1873) 151-. 

 representation by curvilinear arcs. M 1 Cowan, 



J. Edinb. Mth. S. P. 9 (1891) 55-. 



of functions by 



F (x) = S (A P cosp am ^ + B p sin p am V 



Gylden, J. A. H. C. B. 92 (1881) 213."^ 

 , geometric. Catalan, E. C. Liege S. Sc. 



Mm. 15 (1888) No. 1, 68-. 

 and series. Catalan, E. C. Liege S. Sc. Mm. 



13 (1886) 119-, 399. 

 system, as functions of absolute invariant. 



Pincherle, S. Em. E. Ac. Line. Ed. 7 (1891) 



(Sem. 1) 74-. 

 theory. Unferdinger, F. Arch. Mth. Ps. 54 



(1872) 459-. 



. Cayley, A. Mth. A. 12 (1877) 143-. 

 , elementary. Lerch, M. Par. EC. Norm. 



A. 6 (1889) 263-. 

 , new. Weiler, A. Grunert Arch. 35 



(I860) 408-. 

 transformation. Cayley, A. Camb. and Dubl. 



Mth. J. 5 (1850) 204- ; Crelle J. 55 (1858) 



15. 



to normal form, and substitutions of 1st 

 order. Richelot, F. J. Crelle J. 34 (1847) 1-. 



Weierstrass's form. Pittarelli, G., & 

 Brioschi, . Em. E. Ac. Line. Ed. 4 

 (1888) (Sem. 1) 703-. 



Weierstrass's. Fiske, T. S. [1891] A. Mth. 

 6 (1891-92) 7-. 



ydy Clausen, T. As. Nr. 19 



/ - ^7= 



7 (7/ 3 + 8)\V-l 



(1842) 177-. 



dx -f-\/(:c + a) (x + b) (x + c), geometrical repre- 



sentation. Cayley, A. Ph. Mg. 5 (1853) 

 281-. 



dx+\(m-x) (x + a)(x + b) (x + c). Cayley, A. 

 Ph. Mg. 6 (1853) 103-. 



(sinamw) 2r dM, reduction. Thomae, C. J. 

 Crelle J. Mth. 81 (1876) 81-. 



d ^ 2 du. Hermite, C. [1880] As. 

 Nr. 101 (1882) 17-. 



