4440 



Funtions, arbitrary, expressed by double in- 

 tegrals. Meyer, A. [1850] Crelle J. 43 (1852) 

 60-. 



, class, represented by definite integrals. 

 Goursat, E. [1882] Acta Mth. 2 (1883) 1-. 



, expansion, by definite integrals. Lorenz, L. 

 Mth. Ts. 2 (1860) 161-. 



, in form of definite integrals. Pochhammer, 

 L. Crelle J. Mth. 104 (1889) 152-. 



Gamma and related functions. Scheeffer, L. 

 Crelle J. Mth. 97 (1884) 230-. 



G (r, v) -integrals, calculation. Brit. Ass. Comm. 

 (Pearson, K.). B. A. Up. (1896) 70-. 



, tables. Brit. Ass. Comm. (Pearson, K.). 



B. A. Kp. (1899) 65-. 



Integral and sum between same limits, dif- 

 ference. Imschenetsky, V. G. G. Mt. 9 

 (1871) 87-. 



Laplace's transformation and applications. 

 Pincherle, S. Bologna Ac. Sc. Mm. 8 (1887) 

 125-. 



Toroidal functions. Hicks, W. M. Phil. Trans. 

 172 (1882) 609-. 



Automorphic Functions 



4440 



Transcendental 



jendental function I -.- = 1. 



, C. F. [1874] Ups! S. Sc. N. 



= 1. Lind- 

 Acta 9 



(1875) (No. 5) 48 pp. 



sidered by 



functions considered by Legendre, two. 

 Lerch, M. Prag Sb. (1893) (Hth.-Nt.) No. 25, 

 5pp. 



Transcendents arising from integration of ho- 

 mogeneous functions. Winckler, A. [1864] 

 Wien Sb. 50 (1865) (Ab. 2) 531-. 



P (u ; v a , v 2 , . . . v p ; c z , c 2 , . . . c p ; s) . Lerch, M. 

 Prag Sb. (1893) (Mth.-Nt.) No. 24, 7 pp. 



4440 Automorphic functions. 

 (See also 1210, 4050.) 



Burnside, W. [1891-92] L. Mth. S. P. 23 



(1892) 49-, 281-. 



Stackel, P. Crelle J. Mth. 112 (1893) 287-. 

 Abelian functions, generalisation. Picard, E. 



C. E. 98 (1884) 665-. 

 Algebraic surf aces, class. Humbert, G. Palermo 



Cir. Mt. Ed. 4 (1890) 54-. 

 Analogue to exponential function. Alekseevskij , 



V. P. Kharkov Mth. S. Com. 4 (1895) 253- ; 



Fschr. Mth.' (1895) 466. 

 Automorphic elementary forms. Fricke, R. 



Gott. Nr. (1900) 303-. 



forms of arbitrary class. Ritter, E. Gott. 

 Nr. (1893) 120-. 



function groups, application of ideals to. 

 Fricke, R. Gott. Nr. (1894) 106-. 



functions of two variables. Picard, E. 

 Acta Mth. 1 (1882) 297-; C. E. 96 (1883) 

 320- ; C. E. 97 (1883) 1045-. 



n variables, theory. Wirtinger, W. 



Wien Ak. Sb. 108 (1899) (Ab. 2o) 1239-. 



prime forms, representation in theta-series. 

 Burkhardt, H. Mth. A. 42 (1893) 185-. 



Connexion with algebraic functions. Whittaker, 

 E. T. [1898] Phil. Trans. (A) 192 (1899) 1-. 



Cyclic linear transformation. Ermakov, V. P. 



Eec. Mth. (Moscou) 14 (1890) 427-. 

 Differential equations of 3rd order satisfied 



by automorphic functions. Hurwitz, A. 



Mth. A. 33 (1889) 345-. 

 Equations in 2 variables, automorphic for a 



system of rational uniform transformations. 



Schwarz, C. H. A. Crelle J. Mth. 87 (1879) 



139-. 

 , . Hettner, 



G. Gott. Nr. (1880) 386-. 



Fuchsian functions. 



Poincare, H. C. E. 92 (1881) 333-, 395-, 



957, 1198-, 1274-, 1484- ; 93 (1881) 301-, 



581- ; 94 (1882) 163-, 1038-, 1166- ; 95 



(1882) 626- ; 96 (1883) 1485- ; Acta Mth. 1 



(1882) 193-. 



Mittag-Leffler, G. B. A. Ep. (1894) 577. 

 application, and properties. Poincare, H. 



C. E. 92 (1881) 859-. 

 of two complex variables. Kgpinski, S. [1895] 



Krk. Ak. (Mt.-Prz.) Ez. 10 (1896) 211- ; 



Mth. A. 47 (1896) 573-. 

 and equation V-u = e u . Poincare, H. C. E. 



126 (1898) 627-. 

 existence, theorem. Bagnera, F. Ev. Mth. 6 



(1896-99) 31-. 



of first family, representation by infinite pro- 

 ducts. Biermann, 0. Mh. Mth. Ps. 1 (1890) 



49- ; 3 (1892) 143-. 

 hyperfuchsian functions. Picard, E. C. E. 98 



(1884) 563-. 

 , cases. Picard, E. C. E. 101 (1885) 



1127-. 

 in hypergeometric series of two variables. 



Picard, E. C. E. 99 (1884) 852- ; Par. EC. 



Norm. A. 2 (1885) 357-; Par. S. Mth. Bll. 



15 (1887) 148-. 

 . Levavasseur, . 



C. E. 115 (1892) 1006-. 

 and ternary quadratic forms. Picard, E. 



Acta Mth. 5 (1884) 121-. 



and indefinite ternary quadratic forms. Poin- 

 care, H. C. E. 102 (1886) 735-. 

 and quadratic forms. Picard, E. Am. J. Mth. 



11 (1889) 187-. 

 . Stouff, X. Toul. Fac. Sc. A. 8 



(1894) D, 20 pp. 

 theory. Poincare, J. H. (xn) Caen Ac. Mm. 



(1882) 3-. 

 . Biermann, 0. Wien Ak. Sb. 92 (1886) 



(Ab. 2) 1137-. 

 . Schlesinger, L. Mth. Termt. Ets. 6 (1888) 



36- ; Mth. Nt. B. Ung. 6 (1889) 337- ; Crelle 



J. Mth. 105 (1889) 181- ; C. E. 114 (1892) 



1100-, 1409-. 



, Poincare's. Weber, H. Gott. Nr. (1886) 359-. 

 _, _ (Weber). Cassel, G. Stockh. Ak. Hndl. 



Bh. 16 (Afd. 1) (1891) No. 2, 16 pp. ; Fschr. 



Mth. (1891) 438. 

 theta-fuchsian functions. Ovidio, E. d\ Tor. 



Ac. Sc. At. 29 (1894) 741-. 

 transformation. Poincare, H. C. E. 102 (1886) 



. Stouff , X. Par. EC. Norm. A. 5 (1888) 219-. 



350 



