4040 



Elliptic and Single Theta Functions 



logarithmic derivatives of higher order. Ber- 



tolani, G. G. Mt. 34 (1896) 135-. 

 products of 3 and 4. Scheibner, W. Crelle J. 



Mth. 102 (1888) 255-. 

 representation of invariants. Bolza, O. Gott. 



Nr. (1887) 418- ; Mth. A. 30 (1887) 478-. 

 motion of top. Marcolongo, R. G. 



Teix. J. Sc. 14 (1900) 169-. 

 quotient of two. Thomae, J. Mth. A. 



6 (1873) 603-. 

 resolution into factors. Humbert, G. C. B. 



126 (1898) 394-. 

 resultants and discriminants. Schlesinger, 0. 



Mth. A. 33 (1889) 411-. 

 and sigma functions, logarithmic derivatives of 



higher order than 2nd. Bertolani, G. G. 



Mt. 33 (1895) 139-. 

 , and orthogonal systems. Caspary, F. 



Liouv. J. Mth. 6 (1890) 376-. 

 theorem, fundamental. Craig, T. [1891] 



J. H. Un. Cir. [11 (1891-92)] 42. 

 , , Jacobi's. Caspary, F. C. B. 104 



(1887) 1094-. 

 theorems. Lerch, M. Mh. Mth. Ps. 9 (1898) 



177-. 



theory. Enneper,A. Z. Mth. Ps. 12 (1867) 79-. 

 .exposition. Caspary, F. C.B. Ill (1890) 225-. 

 , illustration. Cayley, A. Mess. Mth. 7 



(1878) 27-. 



triple. Cayley, A. Mess. Mth. 7 (1878) 48-. 

 vanishing of. Riemann, [G. F.~] B. [1865] 



Crelle J. 65 (1866) 161-. 



even. Frobenius, G. Gott. Nr. (1888) 67-. 



of one variable, algebraic identities used to 



obtain relations for. Caspary, F. Mth. A. 



28 (1887) 493-. 

 , expression of orthogonal systems by. 



Caspary, F. C. B. 107 (1888) 859-, 934. 

 with fractional characteristics. Voss, 



R. Arch. Mth. Ps. 4 (1886) 385-. 

 zero value. Cayley, A. Crelle J. Mth. 100 



(1887) 87-. 

 for zero values, relations of derivatives. 



Pascal, E. A. Mt. 24 (1896) 23-. 

 and zeta functions, values for certain values of 



argument. Glaisher, J. W. L. E. S. P. 29 



(1879) 351-. 



Theta products, relations. (Jordan, P. [1865] 



Crelle J. 66 (1866) 185-. 

 , , linear. Krazer, A. Acta Mth. 17 



(1893) 281-. 



series, analogy, and some special Heine's 

 hypergeometric series. Lerch, M. [1893] 

 Prag Cesk6 Ak. Fr. Jos. Ez. (Tfida 2) 3 



(1894) Art. 5, 10 pp.; Fschr. Mth. (1893-94) 

 794. 



, and connexion with double integrals. 



Lipps, G. F, Leip. Mth. Ps. B. 44 (1892) 



340-, 473-. 

 , constant factors. Frobenius, G. Crelle 



J. Mth. 98 (1885) 244-. 

 , , in casep = 3. Klein, F. L. Mth. 



S. P. 20 (1889) 235-. 

 series, convergence. Krazer, A. Mth. A. 



49 (1897) 400-. 



4040 



Transcendental functions. Bidone, G. Tor. 



Mm. Ac. 23 (1818) 295-; 24 (1820) 255-. 

 . Jacobi, C. G. J. As. Nr. 6 (1828) 33-; 



Crelle J. 3 (1828) 376- ; 15 (1836) 199-. 



. Clausen, T. As. Nr. 19 (1842) 181-. 



, calculation. Petersen, J. P. C. (xn) 



Ts. Mth. 6 (1876) 1-. 

 , comparison, theory. Ellis, R. L. B. 



A. Ep. (1846) 34-. 

 and their Fourier developments. Kry- 



gowski, Z. Prace Mt.-Fiz. 5 (1894) 70-. 



having property 



/(* + )=/(*),/(* + <>')=/(*), 8(z), 



S(z) denoting a doubly periodic function. 



Picard, E. C. E. 86 (1878) 657-. 



, representation by arcs of curves. 

 Allegret, [A]. Par. EC. Norm. A. 2 (1873) 

 149-. 



space-coordinates, class. Staude, 0. Acta 

 Mth. 10 (1887) 183-. 



Transformation formula 



y = sin (L + A + B + C + ...), 

 some consequences. Griffiths, J. L. Mth. 

 S. P. 17 (1887) 11-. 



Values of integrals in terms of fc 2 . Glaisher, 

 J. W. L. Mess. Mth. 22 (1893) 145-. 



Weierstrass's equation of three terms, generali- 

 sation. Morley, F. N. Y. Am. Mth. S. Bll. 



2 (1896) 21-. 

 formula. Picard, E. 



Bll. Sc. Mth. 24 



(1900) 30-. 

 formulae applied to binary quart* 



cubic. Baker, H. F. QJ. Mth. 24 (1890) 1-. 



formulae applied to binary quartic and ternary 



al(x) functions. Cayley, A. Liouv. J. 

 Mth. 7 (1862) 137-. 



, expansion in powers of variable. 

 Andre, D. Liouv. J. Mth. 5 (1879) 31-. 



Zeta-function. Glaisher, J. W. L. [1885-86] 

 Camb. Ph. S. P. 5 (1886) 221- ; Mess. Mth. 

 15 (1886) 92-. 



, complex, map; a condenser problem. 

 Michell, J. H. Mess. Mth. 23 (1894) 72-. 



-- , process of squaring. Glaisher, J. W. L. 

 Mess. Mth. 16 (1887) 150-. 



I fl X 

 Richelot, A. Crelle J. 32 (1846) 213-. 



' reduction to elli P tic integrals. 



lcnf^** f**W)BinosW 

 10g UJtf' Jo l-fc'sinV etC ' 



Roberts, W. Liouv. J. Mth. 11 (1846) 343-. 



y- 1 2.^. , reduction to elliptic integral of tri- 



J \X 



gonometric form. Plana, G. Crelle J. 36 

 (1848) 1-. 



2?L + ^=0. Cayley, A. L. Mth. S. P. 8 



vz vr 



(1877) 184-. 



= , integration formulae. Cayley, A. [1878] 

 Mess. Mth. 8 (1879) 60-. 



= , Eichelot's integral. Cayley, A. Mess. 

 Mth. 23 (1894) 42-. 



, reduction to elliptic integral. 



(l- 



Cayley, A. Mess. Mth. 11 (1882) 142-. 



324 



