4400 



Other Special Functions. General 



Theta functions of 3 variables. Borchardt, 

 C. W. [1878] Crelle J. Mth. 87 (1879) 169-. 



' . Krause, M. C. K. 131 (1900) 



1188-. 



, algebraic investigations. 

 Schottky, F. Crelle J. Mth. 105 (1889) 269-. 



4 variables. Noether, M. Erlang. 



Ps. Md. S. Sb. 10 (1878) 87-; Mth. A. 14 



(1879) 248-. 



n variables. Noether, M. Mth. A. 16 



(1880) 270-. 



. Poincare", H. Par. S. Mth. 



Bll. 11 (1883) 129-. 

 . Frobenius, G. Crelle J. Mth. 



96 (1884) 100-. 

 , addition theorem. Frobenius, 



G. Crelle J. Mth. 89 (1880) 185-. 

 , . Caspary, F. Crelle J. 



Mth. 97 (1884) 165-. 

 , definition. Schottky, F. Crelle 



J. Mth. 107 (1891) 117-. 

 , formation of orthogonal systems 



by. Caspary, F. C. R. 104 (1887) 490-. 

 , reduction to theta functions of 



fewer variables. Appell, P. Par. S. Mth. 



Bll. 10 (1882) 59-. 

 , theory. Caspary, F. Crelle J. 



Mth. 96 (1884) 324-. 



, transformation, principal. 

 Frobenius, G. Crelle J. Mth. 95 (1883) 264-. 



, vanishing. Tichomandritzky, 



M. A. [1900] N. Y. Am. Mth. S. Bll. 7 



(1901) 64-. 

 p variables. Dalwigk, F. von. Ac. 



Nt. C. N. Acta 57 (1892) 221-. 

 , addition theorem. Stahl, H. 



Crelle J. Mth. 88 (1880) 117-. 



series, convergence. Thomae, C. J. Z. 

 Mth. Ps. 25 (1880) 43-. 



, ra-tuple, infinite, theory. Meissel, E. 

 Crelle J. 48 (1854) 324-. 



Uniform functions with several non-inter- 

 changeable periods. Rausenberger, 0. Mth. 

 A. 20 (1882) 187- ; 21 (1883) 59- ; 25 (1885) 



d log 0(0, 0, ... 0), determination by class- 

 moduli. Thomae, J. [1865] Crelle J. 66 

 (1866) 92-. 



(0, 0, ... 0), determination by class-moduli of 

 algebraic functions. Thomae, J. [1869] 

 Crelle J. 71 (1870) 201-. 



<f> (x, y,z) = ,'S e w*+*w*+<iw8+4m > zeros . 



Rivereau, n U'~albe) . Mars. Fac. Sc. A. 2 

 (1892) 59-. 



p (Mi + M 2 +...2n)> expression by means of a 

 Pfaffian. Fontene, G. Par. EC. Norm. A. 

 13 (1896) 469-. 



Other special functions. 

 4400 General. 



Bernoullians, Baabe's. Dickson, J. D. H. 



[1888] L. Mth. S. P. 20 (1889) 14-. 

 Bernoulli's function. Hermite, C. [18741 Crelle 



J. Mth. 79 (1875) 339-. 



4400 



Bernoulli's function. Glaisher, J. W. L. QJ. 

 Mth. 29 (1898) 1-. 



, Baabe's monograph. Saalschiitz, L. 

 Z. Mth. Ps. 42 (1897) 1-. 



, and its use in semi-convergent series. 



Schlomilch, O. Schlomilch Z. 1 (1856) 193-. 



functions. Imschenetsky , V. G. G. Mt. 

 9 (1871) 87-. 



. SchrSder, . D. Nf. Vh. (1890) (Th. 



2) 5-. 

 , application to series. Berger,A. Stockh. 



Ofv. (1891) 523- ; Fschr. Mth. (1891) 274. 



with arbitrary indices. Sincov, D. 

 Kazan S. Ps.-Mth. Bll. 1 (1891) 234-; Fschr. 

 Mth. (1892) 404-. 



, class of functions related to. Beaupain, 



J. Brux. Mm. Cour. 4, 59 (1901) (Pt. 1) 



33 pp. 



, connection with Biemann's surface. 

 Jonquiere, A. [1890] Stockh. Ak. Hndl. 

 Bh. 16 (Afd. 1) (1891) No. 6, 28 pp. 



, definitions. Renfer, H. Bern Mt. 

 (1900) 1-. 



, expansion in. Rogel, F. Arch. Mth. 



Ps. 17 (1900) 129- . 



, generalisation. Imshenetsky, V. G. 

 St Pet. Ac. Sc. Mm. 31 (1883) No. 11, 

 58 pp. 



and numbers. Berger, A. Stockh. Ak. 



Handl. Bh. 13 (Afd. 1) (1888) No. 9, 43 pp. ; 

 Stockh. Ofv. (1888) 433-; Acta Mth. 14 

 (1890-91) 249-. 



, resolution into partial fractions. 

 Worpitzky, J. Z. Mth. Ps. 29 (1884) 45-. 



polynomial. Plainer, G. Mil. I. Lomb. 

 Ed. 25 (1892) 1179-. 



polynomials. Sonin, , & Hermite, . 

 Crelle J. Mth. 116 (1896) 133-. 



, approximate values. Appell, P. N. A. 



Mth. 6 (1887) 547-. 

 and numbers. Pietrocola, C. G. Mt. 



34 (1896) 48-. 



Functional operations represented by definite 

 integrals. Pincherle, S. Acta Mth. 10 

 (1887) 153-. 



Functions allied to trigonometric functions. 

 Knar, J. Grunert Arch. 27 (1856) 365-. 



analogous to algebraic functions, property. 

 Picard, E. C. B. 89 (1879) 1106-. 



functional determinants. Rosanes, J. 



[1872] Crelle J. 75 (1873) ^166-. 



with lacunae. Goursat, E. Bll. Sc. Mth. 

 11 (1887) 109-. 



. Poincare; H. Am. J. Mth. 14 



(1892) 201-. 



. Cayley,. QJ. Mth. 26 (1893) 279-. 



. Krygowski, Z. Par. S. Mth. Bll. 



25 (1897) 240- ; PraceMt.-Fiz. 9 (1898) 213- ; 



Fschr. Mth. (1898) 352. 

 . Pscheborsky, A. P. Fschr. Mth. 



(1897) 357. 

 , case. Goursat, E. Bll. Sc. Mth. 



17 (1893) 247-. 

 , Goursat's theorem. Pszeborsky, A. P. 



Fschr. Mth. (1897) 356-. 



lacunary circle. Gomes Teixeira, F. 

 Bll. Sc. Mth. 17 (1893) 29-. 



338 



