4040 



Elliptic and Single Theta Functions 



g-series for kp sn u, kp en u, p dn u, process for 



squaring. Glaisher, J. W. L. Mess. Mth. 



16 (1887) 145-. 

 Quadratic forms, Kronecker's theorems. Her- 



mite, C. Liouv. J. Mth. 9 (1864) 145-. 

 Quadrature of the ellipsoid. Carda, K. Mh. 



Mth. Ps. 7 (1896) 129-. 

 Quadri-quadric porism. Matheics, G. B. QJ. 



Mth. 30 (1899) 16-. 

 Eational functions of elliptic form. Pokrovskij, 



P. M. [1900] Rec. Mth. (Moscou) 21 (1901) 



387-; Fschr. Mth. (1900) 445. 

 Rectangular transformation, Wilkinson's. 



Cayley, A. L. Mth. S. P. 14 (1883) 222-. 



Reduction of j- , when U is of fourth order. 



Cayley, A. Camb. and Dubl. Mth. J. 1 



(1846) 70-. 

 Relation of Jacobi, arithmetical deduction. 



Lipschitz, E. Acta Mth. 7 (1885) 95-. 

 Legendre. Kronecker, L. Berl. Ak. Sb. 



(1891) 323-, 343-, 447-, 905-. 

 Rotation of body, theory. Marcolongo, It. 



Palermo Cir. Mt. Rd. 7 (1893) 26-. 

 Segner's numbers. Catalan, E. C. Li6ge S. 



Sc. Mm. 15 (1888) No. 1, 113-. 

 Series representing the twelve elliptic and the 



four zeta functions. Glaisher, J. W. L. 



Mess. Mth. 18 (1889) 1-. 

 Sigma function. Tognoli, 0. G. Mt. 25 (1887) 



367-. 

 , general function satisfying equation for. 



Delisle, A. Mth. A. 30 (1887) 91-. 



, Weierstrass's fundamental theorem. 

 Caspary, F. Crelle J. Mth. 96 (1884) 182-. 



functions. Loria, G. G. Mt. 31 (1893) 

 179-. 



of several arguments, new method. 

 Jahnke, E. Z. Mth. Ps. 37 (1892) 178-. 



, elliptic, as special case of hyperelliptic 



(r-functions. Bolza, 0. N. Y. Am. Mth. S. 

 T. 1 (1900) 53-. 



, even. Pascal, E. A. Mt. 23 (1895) 



181-. 



, , Brioschi's recursion formula for 

 expansion. Bolza, O. Am. J. Mth. 21 

 (1899) 175-. 



, expression of orthogonal system by, and 



application to rotation. Jahnke, E. Liouv. 

 J. Mth. 5 (1899) 155-. 



, general, formation. Krazer, A. Mth. 

 A. 33 (1889) 591-. 



functions and theta functions, Weierstrass's, 

 properties. Lerch, M. Prag Sb. (1887) 

 (Mth.-Nt.) 426-. 



series, Weierstrass's, numerical coeffi- 

 cients in. Haussner, B. Gott. Nr. (1894) 

 299-. 



a (u), Weierstrass's, and allied functions. 

 Kluyver, J. C. N. Arch. Wisk. 3 (1898) 

 80-; Fschr. Mth. (1897) 392. 



Sine of amplitude, inverse and square, ex- 

 pansion in powers of the variable. Hermite, 

 C. As. Fr. C. R. (1875) 131-. 



Subsidiary elliptic function pm (u, k). 

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

 219-. 



4040 



Symmetric functions of I, G, E in terms of 



Q. Glaisher, J. W. L. Mess. Mth. 21 



(1892) 65-. 

 Theorem of Dirichlet. Cayley, A. Camb. and 



Dubl. Mth. J. 9 (1854) 163-. 

 Poncelet on \/a + bx + ex 2 . Sylvester, 



J. J. Ph. Mg. 20 (1860) 307-. 



THETA FUNCTIONS. 



attached to plane algebraic curve without 



singularities. Pick, G. Wien Ak. Sb. 94 



(1887) (Ab. 2) 739-. 

 breaking up into products of such functions, 



after transformation. Wiltheiss, E. Mth. 



A. 26 (1886) 127-. 

 of class 3. Thomae, J. Leip. Mth. Ps. B. 39 



(1887) 100-. 

 connexion with elliptic integrals. Scheibner, W. 



Leip. Mth. Ps. B. 41 (1889) 86-, 245-. 

 constant factor in expression of (x) as an 



infinite product. St Germain, A. de. [1873] 



Par. S. Mth. Bll. 2 (1874) 62-. 

 differential equation and expansion. Wiltheiss, 



E. Mth. A. 29 (1887) 272-. 

 elliptic constant (0). Thomae, J. Z. Mth. 



Ps. 11 (1866) 247-. 



and eta functions, expansion by products. 



i. Bll. 15 

 216-. 



Presle, de. Par. S. Mth. 



(1887) 



evaluation, and integrals of 2nd kind. Eoch, 



G. Z. Mth. Ps. 11 (1866) 53-. 

 expression as definite integrals. Glaisher, J. 



W.L. [1877] Camb. Ph. S. P. 3 (1880) 61-. 



, series summation leading to. 

 Glaisher, J. W. L. B. A. Rp. (1876) (Sect.) 

 15-; Camb. Ph. S. P. 6 (1889) 129-. 



of direction-cosines of two orthogonal systems 

 of coordinates by. Kotter, F. Berl. Ak. Sb. 

 (1895) 807- ; Crelle J. Mth. 116 (1896) 213-. 



elliptic integrals of 2nd and 3rd kinds by. 



Eoch, G. Z. Mth. Ps. 10 (1865) 317-. 

 Euler's angles by. Caspary, F. Bll. Sc. 



Mth. 13 (1889) 89-. 

 (x) as definite integral. Glaisher, J. 



W. L. Mess. Mth. 5 (1876) 173; 17 (1888) 



152-. 



formula. Craig, T. Am. J. Mth. 5 (1882) 350-. 

 , fundamental, new demonstration. Kapteyn, 



W. Bll. Sc. Mth. 15 (1891) 125-. 



of Hermite. Humbert, G. [1880] Par. S. 

 Mth. Bll. 9 (1881) 42-. 



, Jacobi's. Gutzmer, A. Crelle J. Mth. 110 



(1892) 177-. 

 , , geometrical proof. Baker, H. F. Mth. 



A. 43 (1893) 593-. 

 formulae, general. Krazer, A. Mth. A. 52 



(1899) 369-. 

 , Jacobi's. Kronecker, L. Crelle J. Mth. 



102 (1888) 260-. 

 with fractional characteristics. Krause, M. 



Mth. A. 26 (1886) 569-. 

 integration by. Appell, P. C. R. 90 (1880) 



1207-. 

 Jacobi's. Frenet, F. Bordeaux Mm. S. Sc. 8 



(1870) 177-. 

 ^ , theory. Herstowski, F. Mth. A 11 



(1877) 1-. 



323 



x2 



