4040 



Elliptic Integrals 



4040 



&(u), application to Poncelet's polygons. 



Vivanti, G. Palermo Cir. Mt. Ed. 7 (1893) 61-. 

 Z(M), 9(w), n (M, a). Glaisher, J. W. L. 



L. Mth. S. P. 17 (1887) 152-. 

 6) (u : g n , g 3 ). Soderblom, A. Ups. S. Sc. N. 



Acta 17 (1898) No. 6, 56 pp. 



a,(x)- Sna; - d . Grave, D. Fschr. Mth. 

 v cna; 

 (1899) 402. 



Elliptic and hyper-elliptic systems of differential 

 equations, etc. Roberts, W. R. W. L. Mth. 

 S. P. 26 (1895) 379-. 



Elliptic integrals. 



Lobatto, R. (via) Amst. N. Ws. Ntk. Vh. 



I (1844) 70-. 



Genocchi, A. Schlomilch Z. 2 (1857) 414-. 

 Enneper, A. Z. Mth. Ps. 11 (1866) 74-; 



Mth. A. 11 (1877) 567-. 

 Thomae, C. J. Z. Mth. Ps. 23 (1878) 409-. 

 Enneper, A. Gott. Nr. (1884) 175-. 

 Heymann, W. Crelle J. Mth. 103 (1888) 87-. 

 Catalan, E. Brux. Ac. Mm. 49 (1890-93) 



(No. 6) 20 pp. 

 algebraic equations leading to. Jolianson, A. M. 



Stockh. Ofv. (1887) 691- ; Fschr. Mth. (1887) 



448. 

 and arc and logarithm, representation by 



infinite products. Seidel, L. [1867] Crelle 



J. 73 (1871) 273-. 

 cases. Schlomilch, 0. X. Z. Mth. Ps. 27 



(1882) 62-. 

 class of integrals allied to. Ramus, C. Kiob. 



Ov. (1834-35) 2-; (1835-36) 4-; Kiob. Dn. 



Vd. Selsk. Afh. 6 (1837) 249-, 265-. 

 complete, and gamma functions, definite in- 



tegrals expressible by. Glaisher, J. W, L. 



L. Mth. S. P. 12 (1880-81) 92-. 

 condition that an algebraic equation shall 



lead to. Johanson, A. M. Stockh. Ofv. 



(1887) 703- ; Fschr. Mth. (1887) 448. 

 elliptic functions for. Baraniecki, M. A. 



Par. T. Nauk So. Pam. 7 (*1875) Art. 5, 



8 pp. 

 and elliptic functions, connexion with ellipse. 



ImSeneckij, V. G. St Pet. Ac. Sc. Mm. 



(Rs.) 48 (1884) (Suppl.) No. 5, 43 pp.; 



Fschr. Mth. (1884) 652. 

 --- in connexion with theory of catenary, 



transformations. Oekinghaus, E. Arch. 



Mth. Ps. 2 (1885) 138- ; 4 (1886) 225-. 

 --- , evaluation by transformation of 2nd 



degree. Kluyver, J. C. Par. EC. Norm. A. 



II (1894) 37-. 



--- ', representation, geometrical. Grave, P. 



Kazan S. Ps.-Mth. Bll. 4 (1895) 43-, 159- ; 



Fschr. Mth. (1893-94) 768. 

 equivalence of forms of quadratures of differ- 



entials reducible to. Salvert, F. de. C. B. 



120 (1895) 1034-. 

 evaluation by arithmetico-geometric mean. 



Kowalczyk, J. Wiad. Mt. 2 (1898) 21-. 

 expansion in series, and comparisons. Schulze, 



N. W. Grunert Arch. 19 (1852) 181-. 



expansion by zonal harmonics. Hargreaves, R. 

 Mess. Mth. 26 (1897) 89-. 



of (a 2 + b 2 - 2abcos 0) n+i by. Wallace, (Prof.) 

 W. [1802] Edinb. B. S. T. 5 (1805) 253-. 



expression as definite integrals. Zurria, G. 

 Bm. S. It. Mm. 8 (1892) No. 3, 18 pp. 



in finite form. Bugaev, N. V. [1891] Bee. 

 Mth. (Moscou) 16 (1893 259-; Fschr. Mth. 

 (1892) 421-. 



of line-element by. Selander, E. Helsingf. 

 Ofv. 34 (1892) 203-. 



formula y - sin (A + B + C +...), deduction from. 



Griffiths, J. L. Mth. S. P. 15 (*1883-84) 



78-. 

 = , (Griffiths). Cayley, A. 



L. Mth. S. P. 15 (*1883-84) 81. 

 formulas. Cayley, A. Mth. A. 12 (1877) 



369-. 



. Torelli, G. A. Mt. 15 (1887-88) 67-. 

 as functions of modulus. Torelli, G. G. Mt. 



12 (1874) 168-. 

 general forms. Scheibner, W. Leip. Mth. 



Ps. B. 43 (1891) 575-. 



geometrical, analytical and dynamical signi- 

 ficance. Oekinghaus, E. Arch. Mth. Ps. 



I (1884) 337-; 4 (1886) 279-. 



and hyperelliptic integrals. Neumann, C. 



[1870] Mth. A. 3) 1871) 611-. 

 . Oekinghaus, E. Arch. Mth. Ps. 



II (1892) 132-. 



with imaginary modulus. Hermite, . [1890] 

 Hamb. Mth. Gs. Mt. 3 (1900) 22-. 



parameters. Booth, J. Ph. Mg. 7 

 (1854) 213-. 



in indeterminate form, two. Darboux, G. 



Bordeaux S. Sc. Mm. 3 (1880) 373-. 

 integrals formed from, and their applications. 



Torelli, G. G. Mt. 11 (1873) 17-. 

 integration in finite form. Ptaszycki, J. [1888] 



Bll. Sc. Mth. 13 (1889) 65-. 

 inversion. Pasch, M. Mth. A. 19 (1882) 155-. 

 . Halphen, G. H. Par. EC. Pol. J. 54 



(1884) 171-. 

 , Cauchy's method. Didon, F. Liouv. 



J. Mth. 14 (1869) 230-. 



and irreducibility of periods. Picard, E. 

 Bll. Sc. Mth. 14 (1890) 107-. 



problem. Tlkhomandrltskil, M. A. Kharkov 

 Mth. S. Com. (xn) (1883) 47-; (1884) 187- ; 

 Mth. A. 22 (1883) 450- ; 25 (1885) 197-. 



problems. Lindemann, F. Munch. Ak. Sb. 

 28 (1899) 37-. 



of 1st kind, application of Abel's theorem. 



Burnside, W. Mess. Mth. 21 (1892) 164-. 

 , calculation. Radau, R. Bll. As. 



4 (1887) 99-. 

 , , Legendre's scale. Newntan, F. W. 



B. A. Bp. (1876) (Sect.) 28-. 

 , expansion, and a series of integers. 



Catalan, E. Brux. Ac. Mm. 46 (1886) 



(No. 4) 24 pp. 

 , in trigonometric series. Beaupain, 



J. Lifege S. Sc. Mm. 1 (1899) No. 4, 22 pp. 

 , Gauss's approximation. Freeman, A. 



Mess. Mth. 5 (1871) 245-. 



, illustration by certain link-work. 

 Emch, A. A. Mth. 1 (1900) 81-. 



31$ 



