4070 Multiperiodic Functions. General Theta Functions 4070 



Quadruply periodic functions of 2nd and 3rd 

 kinds. Krause, M. Liouv. J. Mth. 3 (1887) 

 87-. 



satisfying systems of differential 

 equations. Krause, M. N. Y. Am. Mth. S. 

 T. 1 (1900) 287-. 



of 2 variables. Picard, E. C. B. 124 



(1897) 1490-. 

 , of 3rd kind. Appell, P. 



Par. EC. Norm. A. 7 (1890) 143-. 

 series. Picard, E. C. B. 108 (1889) 



659-. 



Eosenhain's fundamental formulas, simple de- 

 monstration. Caspary, F. Mth. A. 30 



(1887) 571-. 

 Sigma functions of 2 variables, expansion in 



series. Brioschi, F. Gott. Nr. (1890) 



236-. 

 Theta characteristics. Noether, M. Erlang. 



Ps. Md. S. Sb. 11 (1879) 198-. 

 , demonstration of theorem of Biemann's. 



Stahl, H. Crelle J. Mth. 88 (1880) 273-. 



constants, 2 variables, certain relations 

 among. Hutchinson, J. I. N. Y. Am. Mth. 

 S. T. 1 (1900) 391-. 



formula, general, derivation. Prym, F. E. 

 Acta Mth. 3 (1883) 216-. 



, Biemann's, demonstration. Prym, F. E. 



[1882] Acta Mth. 3 (1883) 201-. 

 , , derivation. Prym, F. E. Crelle J. 



Mth. 93 (1882) 124-. 

 , , generalisation. Krazer, C. A. J., & 



Prym, F. E. Acta Mth. 3 (1883) 240-. 



function, infinite variety of forms. Weber, 

 H. Crelle J. 74 (1872) 57-. 



functions. Enneper, A. Gott. Nr. (1883) 

 175-, 261-. 



, characteristics. Jordan, C. C. E. 88 



(1879) 1020-, 1068- ; Par. EC. Pol. J. Cah. 



46 (1879) 35-. 

 , of which are formed from thirds of 



integers. Krazer, C. A. J. Mth. A. 22 



(1883) 416-. 

 , double. Cayley, A. [1877-78] Crelle 



J. Mth. 83 (1877) 210-, 220- ; 85 (1878) 214- ; 



87 (1879) 74-. 

 ,, addition. Cayley, A. [1879] Crelle 



J. Mth. 88 (1880) 74-. 



Gott. 



J. Jena. Z. 20 (1887) 581-. 

 , , transformation. Cayley, A. QJ. 



Mth. 21 (1886) 142-. 

 , equation between. Enneper, A. 



Nr. (1878) 550-. 

 , equations for 6 (0, 0, ... 0). Fuchs, L. 



Crelle J. 73 (1871) 324-. 



Theta functions with multiple arguments. 



Eoch, G. Crelle J. 66 (1866) 177-. 

 , multiple, theorem. Cayley, A. Mth. 



A. 16 (1880) 115-. 

 , multiplication of four, formula. Smith, 



H. J. S. L. Mth. S. P. 1 (1866) No. 8, 



14 pp. 



, particularly those of 2 variables. 

 Forsyth, A. E. [1881] Phil. Trans. 173 



(1883) 783-. 



, quadruple. Craig, T. Am. J. Mth. 6 



(1884) 14-, 183-. 



, single and double. Cayley, A. [1879] 



Phil. Trans. 171 (1880) 897-. 

 , theorems, generalisation of two. Elliot, 



Z. C. E. 90 (1880) 352-. 

 , transformation. Frobenius, G. [1879] 



Crelle J. Mth. 89 (1880) 40-. 

 , theory, especially for 3 variables. 



Weber, H. A. Mt. 9 (1878-79) 126-. 

 , triple. Cayley, A. [1878] Crelle J. 



Mth. 87 (1879) 134-, 165-, 190-. 

 , vanishing. Neumann, C. G. Leip. Mth. 



Ps. B. 35 (1883) 99-. 

 of 2 variables. Caspary, F. [1881] 



Crelle J. Mth. 94 (1883) 74-. 

 . Darboux, G. C. E. 92 (1881) 



685-, 1493-. 

 . Schleiermacher, L. Erlang. 



Ps. Md. S. Sb. 18 (1886) 22-. 



. and corresponding Kummer'a 



surface. Schleiermacher, L. Mth. A. 50 

 (1898) 183-. 



, derivatives in terms of squares 



of theta functions. Jahnke, E. C. B. 126 



(1898) 1083-. 

 . , differential relations for. 



Jahnke, E. Leip. Mth. Ps. B. 52 (1900) 140-. 

 , connected with. Krause, 



M. Mth. A. 26 (1886) 1- ; A. Mt. 15 (1887- 



88) 173-. 



, expressions for elements of 



orthogonal system. Jahnke, E. C. B. 126 

 (1898) 1013-. 



, Fourier's series in domain of. 



Krause, M. Mth. A. 27 (1886) 419-. 



and generalised Kummer's 

 surface. Wirtinger, W. Mh. Mth. Ps. 1 

 (1890) 113-. 



, orthogonal system formed from. 



Jahnke, E. Berl. Ak. Sb. (1896) 1023- ; 

 Crelle J. Mth. 119 (1898) 234-. 



, systems for derivatives. 



Jahnke, E. C. E. 125 (1897) 486-. 



, reduction to theta functions of 



one variable. Appell, P. C. E. 94 (1882) 

 421-. 



, form of arguments, and determination '_ ^ relations. Staude, O. Mth. 



of (0, . . . ) as function of class moduli. 



Fuchs, L. Crelle J. 73 (1871) 305-. 

 , function analogous to. Appell, P. 



Mars. Fac. Sc. A. 1 (1892) 47-. 

 , general. Noether, M. [1879] Erlang. 



Ps. Md. S. Sb. 12 (1880) 1-. 

 , . Wirtinger, W. Wien Az. 32 (1895) 



58-. 

 on a general Eiemann's surface. Klein, 



F. C. E. 108 (1889) 277-. 



A. 24 (1884) 281-. 

 , . Igel, B. Mh. Mth. Ps. 2 



(1891) 157-. 

 , between the 16. Schottky, 



F. Crelle J. Mth. 105 (1889) 233-. 

 , transformation. Krause, M. 



Mth. A. 25 (1885) 323-. 

 , , application to arithmetico- 



geometric mean of 4 elements. Hettner, G. 



Crelle J. Mth. 112 (1893) 89-. 



VOL. I. 



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