4470 Integral Functions 



4460 Functions which may he de- 

 fined by functional equations. 

 (See also 6030.) 



Algebraic operations of higher order; e.g. a aetc< 



Schubert, H. C. H. Hamb. Mth. Gs. Mt. 1 



(1889) 62. 

 Formation of a function F (x) having property 



F[<f>(x)]=F(x). Appell.P. C. E. 88(1879) 



807-. 

 Function given by / (z) + a0 (z) = expanded in 



infinite series ; applications. Rodrigues,J.M. 



Fschr. Mth. (1884) 219-. 



f (z) = ---- , definition by a system of 



functional properties. Moore, E. H. A. Mth. 

 9 (1894-95) 43-. 



Functional equations, solutions. Pick, G. 

 Mth. A. 24 (1884) 590-. 



relation (u) . <j> (v) = (u + v) . Wilson, E. B. 

 A. Mth. 1 (1900) 47-. 



Functions satisfying equation 



relations. Magnus, L. J. Crelle J. 5 (1829) 

 365-. 



Lottner, C. L. E. [1850] Crelle J. 46 (1853) 

 367-. 



such that F ( sin 



|. Appell, P. 



C. E. 88 (1879) 1022-. 

 Generalisation, calculus. Oltramare, G. As. 



Fr. C. E. (1887) (Pt. 2) 285-. 

 Integral of function when only characteristic 



functional equation is given. Pexider, J. 



Casopis 29 (1900) 33-; Fschr. Mth. (1900) 



306. 

 Iterative functions. Schroder, E. [1869] Mth. 



A. 3 (1871) 296-. 

 . Lemeray, E. M. As. Fr. C. E. (1895) 



(Pt. 2) 149-. 

 Transcendental function, Soldner's. Buzen- 



geiger, K. H. J. Zach M. Cor. 26 (1812) 285-. 



4470 Integral functions. 



Galois, E. Liouv. J. Mth. 11 (1846) 408-. 

 Picard, E. C. E. 88 (1879) 1024- ; 89 (1879) 



662-; Par. EC. Norm. A. 9 (1880) 145- ; 



Par. S. Mth. Bll., 11 (1883) 136-. 

 Guichard, . Par. EC. Norm. A. 1 (1884) 427-. 

 Vivanti, G. G. Mt. 26 (1888) 303-. 

 Laurent, H. Par. EC. Pol. J. 60 (1890) 107-. 

 Desaint, . C. E. 120 (1895) 548-. 

 Hadamard, . C. E. 122 (1896) 1257-. 

 Laurent, H. N. A. Mth. 15 (1896) 23-. 

 Peter sen, J. Acta Mth. 23 (1900) 85-. 

 Wigert, S. Stockh. Ofv. (1900) 1001-. 

 Divisibility. Koch, H. von. Stockh. Ofv. 



(1893) 449-. 



Integral Functions 4470 



Divisibility of function of n 2 elements by their 

 determinant. Mertens, F. Wien Ak. Sb. 81 

 (1880) (Ab. 2) 260-. 



properties of functions of higher derivatives. 



Meyer, F. Mth. A. 36 (1890) 435-, 



Divisor, common, of two functions of one 

 variable. Netto, E. Crelle J. Mth. 106 

 (1890) 81-. 



Divisors. Mertens, F. Wien Ak. Sb. 97 (1889) 

 (Ab. 2a) 618-. 



Extension of property of polynomials to inte- 

 gral functions. Borel, E. C. E. 123 (1896) 

 556-. 



Factorisaton. Konig, G. [1882] (xn) Mth. 

 Termt. Ets. 2 (1884) 45-. 



and related elimination problems. Konig, 

 J. [G.] Mth. A. 15 (1879) 161-. 



Factors. Selivano/, D. Par. S. Mth. Bll. 13 



(1885) 119-. 

 Function of 2 integral arguments. Muir, T. 



Edinb. Mth. S. P. 3 (1885) 19-. 



satisfying certain conditions, degree. 

 Tchebitchef, P. L. Par. S. Mth. Bll. 3 

 (1875) 103. 



Functions assuming given values at given 

 points. Cazzaniga, P. A. Mt. 10 (1880- 

 82) 279-. 



and continued fractions. Christoffel, E. P. 

 [1876] A. Mt. 8 (1877) 1-. 



of form G(x). Hadamard, . C. E. 114 



(1892) 1053-. 



of m systems each of n variables. Mertens, 

 F. Mh. Mth. Ps. 4 (1893) 193-, 297-. 



and types of increase. Borel, E. C. E. 

 126 (1898) 321-. 



Hilbert's theorem, extension to infinite poly- 

 nomials. Capelli, A. Nap. Ed. 35 (1896) 

 321-. 



Homogeneous functions. Andre, D. Par. S. 

 Phlm. Bll. 1 (1899) 124. 



Irreducibility of functions of integral functions 

 with integral coefficients. Netto, E. Giessen 

 Oberh. Gs. B. 31 (1896) 113- ; Mth. A. 48 

 (1897) 80-. 



Irreducible polynomials. Kahan, W. F. Fschr. 

 Mth. (1899) 100. 



Polynomials satisfying relation of 3rd order. 

 Weill, . N. A. Mth. 4 (1885) 184-. 



Properties. Hadamard, J. Liouv. J. Mth. 9 



(1893) 171-. 



. Desaint, . C. E. 124 (1897) 746-. 

 Eational function, transformation. Laisant, 

 . Par. S. Mth. Bll. 20 (1892) 6-. 



functions, theorems. Grunert, J. A. 

 Grunert Arch. 31 (1858) 27-. 



Eedueible functions of n variables. Meyer, F. 



Mth. A. 30 (1887) 30-. 

 Eeduction. Pellet, A. E. Par. S. Mth. Bll. 



19 (1891) 48-. 



to canonical form of functions of n variables. 

 Mirimanov, D. S. Eec. Mth. (Moscou) 19 

 (1897) 629 (bis)- ; Fschr. Mth. (1897) 88. 



Eesultants of n forms with n variables, deter- 

 mining properties. Mertens, F. Wien Ak. 

 Sb. 93 (1886) (Ab. 2) 527-. 



System of functions A<f> + Bi{/', theorem. 

 Nother, M. [1872] Mth. A. 6 (1873) 351-. 



353 



