4050 Elliptic Functions 



of 7th order, modular equation for. Giitzlaff, 



C. E. Crelle J. 12 (1834) 173-. 

 , , algebraic solution. Ely, G. S. 



L. Mth. S. P. 13 (1882) 153-. 



llth order. Klein, C. F. Mil. I. Lomb. 

 Bd. 12 (1879) 629- ; Mth. A. 15 (1879) 533-. 



. Brioschi, F. A. Mt. 21 (1893) 



309-. 

 , modular equation for. Cayley, A. 



C. B. Ill (1890) 447-. 



periodic functions. Teixeira, J. P. Lisb. 

 J. Sc. Mth. 3 (1895) 1-. 



principle of Jacobi, extension. Ktmigsberger, L. 



[1878] Crelle J. Mth. 87 (1879) 173-. 

 problem for elliptic function of 2nd kind, four 



connected solutions. Salvert, F. de. C. B. 



118 (1894) 1181-. 

 3rd kind, four connected solutions. 



Salvert, F. de. C. B. 118 (1894) 1403-. 



in representation leading to. Thomae, J. 

 Z. Mth. Ps. 18 (1873) 401-. 



, solution. Abel, N. H. As. Nr. 6 (1828) 



365-. 

 quadratic, of elliptic function. Gundelfinger, S. 



[1873] (vii) Mth. A. 7 (1874) 449-. 

 quadric, of elliptic integrals. Kummell, C. H. 



Smiths. Misc. Col. 33 (1888) Art. 2, 102- ; 



(Wash. Ph. S. Bll. 7 (1885).) 

 quartic. Cayley, A. QJ. Mth. 12 (1873) 



266-. 

 to reciprocal and to complementary modulus. 



Johnson, W. W. Mess. Mth. 11 (1882) 138-. 

 simplification of equations. Kiepert, L. Mth. 



A. 37 (1890) 368-. 

 simultaneous, of elliptic integrals. Kuschniriuk, 



M. Mh. Mth. Ps. 8 (1897) 281-. 

 by substitution of a given function of 1st degree, 



number. Abel, N. H. Crelle J. 3 (1828) 



394-. 

 theory. Kiepert, L. Crelle J. Mth. 87 (1879) 



199- ; 83 (1880) 205- ; 95 (1883) 218-. 

 . Hurwitz, A. [1881] Mth. A. 19 (1882) 



. Smith, H. J. S. [1882-83] Mess. Mth. 



12 (1883) 49-; 13 (1884) 1-. 

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



152-. 



. Fricke, R. Mth. A. 40 (1892) 469-. 

 , algebraic. Griffiths, J. [1891] L. Mth. S. 



P. 23 (1892) 275-. 

 , and application to theory of numbers. 



Weber, H. Mth. A. 43 (1893) 185-. 

 , Jacobi's. Griffiths, J. L. Mth. S. P. 15 



(*1883-84) 58-. 

 , results from. Griffiths, J. L. Mth. S. P. 



16 (1884-85) 83-. 

 of theta functions. David, . Liouv. J. Mth. 



6 (1880) 187-. 

 . Miiller, F. Arch. Mth. Ps. 1 (1884) 



161-. 

 . RoMe, F. Arch. Mth. Ps. 3 (1886) 



138-. 

 . Krause, M. Leip. Mth. Ps. B. 45 



(1893) 99-, 349-, 523-, 805- ; 48 (1896) 291-. 

 , Jacobian equations of 40th degree. 



Burkhardt, H. Gott. Nr. (1890) 376-. 

 , problem, special. Krazer, A. Crelle 



J. Mth. Ill (1893) 64-. 



Abelian Functions 4060 



of theta functions, quadratic. Krazer, A. 



Mth. A. 46 (1895) 442-. 

 of one variable. Krause, M. Mth. A. 



25 (1885) 319-. 

 . Krazer, A. Mth. A. 43 



(1893) 413-. 

 verification. Chevallier, J. Camb. Ph. S. P. 



5 (1886) 381-. 



Trigonometric and elliptic functions, expansion 



in partial fractions and infinite products. 



Tichomandrickij, M. A. Kharkov Mth. S. 



Com. 2 (1891) 167- ; Fschr. Mth. (1890) 



450. 

 Weierstrass's elliptic functions, trisection of 



periods for. Burnside, W. Mess. Mth. 16 



(1887) 177-. 



I du ^/[l - A? snc 2 %( a + u) snc2 (a - M)] and 



7 



/ du ^/[l-Psna ( + ) sn2 (-)] 



Gudermann, C. Crelle J. 39 (1850) 50-. 

 Arg. sn a and (arg. sn a) 2 , expression as definite 

 integrals. Glaisher, J. W. L. [1882] QJ. 

 Mth. 19 (1883) 71-. 



4060 Abelian integrals. (See 

 also 8050, 8060.) 



Abelian differential equations in case of reduc- 

 tion of number of periods. Picard, E. C. B. 

 95 (1882) 898-. 



equation, and theorem of Parseval. Prang- 

 hofer, J. Wien Sb. 57 (1868) (Ab. 2) 29-. 



Abelian functions. 



Jacobi, C. G. J. Crelle J. 9 (1832) 394- ; 13 



(1835) 55- ; 30 (1846) 183- ; Liouv. J. Mth. 



11 (1846) 97-. 

 Stem, A. Kiob. Dn. Vd. Selsk. Skr. 1 (1849) 



323-. 



Rosenhain, G. Crelle J. 40 (1850) 319-. 

 Dienger, J. Grunert Arch. 16 (1851) 67-. 

 Davldov, A. Y. [1868] (xn) Bee. Mth. 



(Moscou) 4 (1869-70) (Pt. 1) 287-. 

 Clebsch, R. F. A. [1869] Gott. Ab. 14 (1869) 



75 pp. ; Mth. A. 2 (1870) 193-. 

 Roberts, M. A. Mt. 3 (1869-70) 70-. 

 Poincare, H. C. B. 92 (1881) 958-. 

 Appell, P. C. E. 94 (1882) 1702-. 

 Poincart, H. C. B. 100 (1885) 785- ; Am. J. 



Mth. 8 (1886) 289-. 

 Appell, P. C. B. 103 (1886) 1246-. 

 Poincare, H. C. B. 120 (1895) 239- ; Liouv. 



J. Mth. 1 (1895) 219-. 

 Ermakow, W. P. Fschr. Mth. (1897) 402. 

 addition formula for, explicit form. Salvert, 



F. de. C. B. 116 (1893) 304-, 412. 



theorem. Weber, H. Crelle J. 70 (1869) 

 193-. 



application to continued fractions. Borchardt, 

 C. W. Crelle J. 48 (1854) 69-. 



in geometry. Clebsch, R. F. A. [1863] 

 Crelle J. 63 (1864) 189-. 



329 



