3600 Complex Variables 



Plane n-line, metric theorems. Loud, F. H. 



N. Y. Am. Mth. S. T. 1 (1900) 323-. 

 Point involutions in plane of complex variable. 



Vries, J. de. Mh. Mth. Ps. 3, (1892) 285-. 

 Principles. Eiquier, . Par. EC. Norm. A. 8 



(1891) 59-, 141- ; 9 (1892) 281-. 

 , fundamental. Cellerier, C. Bll. Sc. Mth. 



14 (1890) 142-. 

 , generalisation. Scheffers, G. Leip. Mth. 



Ps. B. 45 (1893) 828-; 46 (1894) 120-. 



of Weierstrass. Pincherle, S. G. Mt. 18 

 (1880) 178-, 317-. 



Problem. Puzyna,J. Fschr. Mth. (1888) 411. 

 Properties. Trzaska, W. Par. T. Nauk Sc. 



Pam. 1 (*1871) 109- ; Bll. Sc. Mth. As. 6 



(*1874) 152-. 

 Eational functions. Beke, E. Mth. A. 47 



(1896) 441-. 

 Real functions of complex variables. Murphy, 



E. Ph. Mg. 2 (1833) 287-. 



, given over any aggregate of points, 

 analytic representation. Phragmen, E. 

 Palermo Cir. Mt. Rd. 14 (1900) 256-. 



part of any function of complex variable. 

 Bougaieff, . Bll. Sc. Mth. 11 (1887) 61-. 



Representation. Fuchs, L. [1872] Crelle J. 



75 (1873) 177- ; 76 (1873) 175-. 

 , approximate forms for. Pincherle, S. 



Bologna Ac. Sc. Mm. 10 (1889) 77-. 

 , conformal. Wagner, H. A. Hamb. Mth. 



Gs. Mt. 1 (1889) 64-. 

 , . , given by quadratic fractional relation. 



Holzmuller, F. G. Mth. A. 18 (1881) 289-. 



by definite integrals, cases. Somigliana, C. 

 Mil. I. Lomb. Rd. 21 (1888) 431-. 



, theory of images. Harris, E. A. A. Mth. 



4 (1888) 65-, 128. 

 Roots considered as functions of a variable 



parameter. Puiseux, V. C. R. 30 (1850) 171. 

 Series representing arbitrary functions in 



separate regions of convergence. Pringsheim, 



A. Mth. A. 22 (1883) 109-. 

 , terms of which are functions of complex 



variable. La Valtee Poussin, C. de. G. 



Teix. J. Sc. 11 (1892) 77-. 

 Simplifications. Pringsheim, A. Mth. A. 47 



(1896) 12 1-. 

 Singular functions, representation, analytic. 



Tonelli, A. Rm. R. Ac. Line. Rd. 1 (1885) 



124-. 



lines of analytic functions. Painleve, P. 

 Toul. Fac., Sc. A. 2 (1888) B, 130 pp. 



points of a certain function. Dell' Agnola, 

 C. A. Ven. I. At. (1898-99) (Ft. 2) 525-, 

 669-. 



Singularities of analytic functions, class. 



Pringsheim, A. Mth. A. 50 (1898) 442-. 

 (two), comparison. Pincherle, S. 



Rm. R. Ac. Line. Rd. 3 (1887) (Sem. 2) 310-. 

 , especially functions defined by 



differential equations. Painleve, P. C. R. 



131 (1900) 489-. 

 , single-valued and general. Chessin, 



A. S. A. Mth. 11 (1896-97) 52-. 

 function depending on two given functions. 



Pincherle, S. Rm. R. Ac. Line. Rd. 8 (1899) 



(Sem. 1) 228-. 



Uniform Functions 3610 



Theorem. Lerch, M. Prag Sb. (1885) (Mth.- 



Nt.) 351- ; Fschr. Mth. (1886) 347. 

 , Abel's, demonstration of non-existence of 



any other. Konigsberger, L. [1885] Munch. 



Ak. Sb. 15 (1886) 462-. 

 , Cauchy's, on roots, two deductions from. 



Mittag-Leffier, G. Stockh. Ofv. 31 (1874) 



No. 7, 23-. 

 , fundamental. Ascoli, G. [1870] A. Mt. 4 



(1870-71) 31-. 

 , new. Jensen, J. L. W. V. Acta Mth. 22 



(1899) 359-. 

 Theorems, two. San-Martino, A. N. A. Sc. 



Nt. 4 (1845) 353-. 

 Total variation in describing contour. Cauchy, 



A. L. C. R. 40 (1855) 651-, 713-, 804-. 

 Transcendental functions, class. Picard, E. 



C. R. 123 (1896) 1035-. 

 , genus zero and genus one. Laguerre, E. 



C. R. 95 (1882) 828-. 

 , integrals. Koenigsberger, L. Gott. Nr. 



(1884) 116- ; Crelle J. Mth. 98 (1885) 97-. 



, , reduction. Koenigsberger, L. Am. 

 J. Mth. 11 (1889) 221-. 



, new, class. Picard, E. Acta Mth. 18 



(1894) 133- ; 23 (1900) 333-. 



, roots being all transcendental numbers. 

 Gegenbauer, L. Wien Ak. Sb. 108 (1899) 

 (Ab. 2a) 423-. 



Transformation, orthomorphic, of circle into 

 itself. Cayley, A. Edinb. Mth. S. P. 8 

 (1890) 91-. 



Transformations, algebraic. Pagani, G. M. 

 Brux. Ac. Bll. 7 (1840) (pte. 2) 50-. 



y=oo 



Weierstrass' s function 2 b"cos(a v Trx). Tauber, 



A. Mh. Mth. Ps. 8 V (1897) 330-. 

 Wronskians, fundamental property. Demoulin, 



A. Mathesis 17 (1897) 62-. 

 <j> (x, y)+ty(x,y)=F(x + iy) , conditions. Dien- 



ger, J. Grunert Arch. 10 (1847) 422-. 

 Tan~' ( + irj) , reduction to form x + iy. Unfer- 



dinger, F. Arch. Mth. Ps. 49 (1869) 478-. 

 , value. Unferdinger, F. Z. Mth. Ps. 14 



(1869) 77-. 

 <j> (x + yi) + <j> (x- yi) , Abel's expression for. 



Glaisher, J. W. L. [1872] Mess. Mth. 2 



(1873) 12-. 



II (x + iy + r), properties. Schlomilch, 0. Leip. 



B. 24 (1872) 26-; Z. Mth._Ps. 17 (1872) 248-. 



<t> (x + y V^l) + <f> (x - y \/^T) , value. Oltra- 



mare, G. As. Fr. C. R. (1885) (Ft. 2) 127-. 



3610 Uniform functions of one 

 variable. 



Bouquet, J., <& Briot, . Par. EC. Pol. J. 



cah. 36 (1856) 85-, 133-, 199-. 

 Bertrand, J. C. R. 48 (1859) 427-. 

 Imshenetskil, V. G. (xii) Kharkov Mth. S. 



Com. (1880) 173-. 

 Farkas, J. C. R. 96 (1883) 1646-. 

 Vivanti, G. G. Mt. 25 (1887) 54-, 232-, 312. 

 Additions to work of Weierstrass and Mittag- 



Leffler. Casorati,F. A. Mt. 10 (1880-82)261-. 



292 



