3210 



Theory of Functions of Real Variables 



3210 



Functions of two real variables. Biermann, 0. 

 Mth. A. 48 (1897) 393-. 



, and the idea of arbitrary 

 function. Borel, E. G. R. 121 (1895) 

 811-. 



, within a finite range. Ascoli, G. 



Mil. I. Lomb. Ed. 22 (1889) 317-, 438-, 686-, 



804-. 

 several real variables, differentiation and 



integration. Bettazzi, R. G. Mt. 22 (1884) 



133-, 200. 



with recurring derivatives. Sang, E. [1866] 

 Edinb. R. S. T. 24 (1867) 523-. 



, representation by a curve (strip). Klein, F. 



(vm) Erlang. Sb. Ps. Md. S. 6 (1874) 



52-. 

 Harmonic functions of two real variables and 



functions of a complex argument, oscillations 



in values. Schottky, E. Crelle J. Mth. 117' 



(1897) 225-. 

 Homogeneous functions, extension of Euler's 



theorem. Philip, W. E. Edinb. Mth. S. P. 



18 (1900) 101-. 

 Implicit functions of a real variable. Ingrami, 



G. Bologna Rd. (1888-89) 108-. 

 , transformation into explicit. Cauchy, 



A. L. C. R. 38 (1854) 944-. 



, monodromic and monogenous. 

 Cauchy, A. L. C. R. 40 (1855) 878-. 



Integral polynomials of one variable. Hermite, 



C. N. Ts. Mth. 5 (B) (1894) 1-. 

 Invariability of form. Maiziere, de. Ger- 



gonne A. Mth. 1 (1810-11) 368-. 

 Irrational functions. Cauchy, A. L. C. R. 32 



(1851) 68-, 162-. 

 Isobaric calculus. Cesdro, E. N. A. Mth. 3 



(1884) 561- ; 4 (1885) 59-, 578. 

 Lagrange's "Theorie des Fonctions Analy- 



tiques," note. Poissan, S. D. Liouv. J. Mth. 



2 (1837) 140-, 189-. 



, , Poisson's. Poinsot, L. 

 C. R. 4 (1837) 559-. 



Limits of functions. Matzka, W. Prag Sb. 



(1878) 262-. 

 , superior, of functions, calculation. Cauchy, 



A. L. C. R. 15 (1842) 138-. 

 Mean value, theorem. Stringham, I. As. S. 



Pac. Pb. 2 (1890) 100- ; 3 (1891) 112. 

 Ordered functions. Somigliana, C. Rm. R. 



Ac. Line. Rd. 8 (1899) (Son. 2) 125-. 

 Principle, fundamental, elementary proof. 



Mansion, P. B. A. Rp. (1876) (Sect.) 



26-. 

 Properties, behaviour, etc. Scheffler, H. 



Grunert Arch. 28 (1857) 121-. 

 , general. Ruffini, P. [1806] Mod. S. It. 



Mm. 13 (1807) 292-. 

 Rational functions, approximate square roots. 



Bugaev, N. V. [1881] (XH) Rec. Mth. 



(Moscou) 10 (1882-83) (Ft. 1) 524-. 



, elements of a theory. Kraus, L. 

 Casopis 14 (1885) 49-; Fschr. Mth. (1885) 

 369-. 



Real non-analytic functions, development. 



Painleve, P. C. R. 126 (1898) 459-. 

 Reciprocal functions. Cauchy, A. L. Par. S, 



Phlm. Bll. (1818) 178-. 



Reciprocal relation of functions. Raabe, J. L. 



[1852] Ztir. Mt. 3 (1853-55) 198-. 

 Simple functions, gradation. Oettinger, L. 



Crelle J. 11 (1834) 75-, 173- ; 12 (1834) 



295-; 13 (1835) 292-. 

 Singularities, new general condensation prin- 



ciple. Cantor, G. Mth. A. 19 (1882) 



588-. 

 Summatorial functions, properties. Hill, 



C. J. D. Sk. Nf. F. 8 (I860) 518-. 

 Sums. (Bjorling.) Folk, M. Ts. Mt. Fys. 4 



(1871) 71-. 

 Systems. Eicci, G. Rm. R. Ac. Line. Rd. 5 



(1889) (Sem. 1) 112-. 



. Stdckel, P. Crelle J. Mth. 112 (1893) 

 311-. 



, inversion. Kneser, A. Mth. A. 45 (1894) 

 446-. 



Theorem. Grolous, J. Par. S. Phlm. Bll. 12 

 (1875) 95-. 



. Tonelli, A. A. Mt. 9 (1878-79) 173-. 



. Poincare, H. Par. S. Mth. Bll. 11 

 (1883) 112-. 



, applications. Krey, H. Z. Mth. Ps. 26 

 (1881) 357-. 



on determination of u, v to satisfy 

 uf(x) + vF(x)=E. Cauchy, A. L. Baum- 

 gartner Z. 1 (1826) 88-. 



Theorems. Prym, F. E. Crelle J. 71 (1870) 

 223-. 



. Thomae, C. J. Gott. Nr. (1878) 466-. 



, two, of Tchebitchef's, generalisation. 

 Minine, A. Les Mondes 55 (1881) 185-. 



Transformation of functions. Deflers, . 



Par. S. Phlm. Bll. (1819) 161-. 

 --- . Nicholson, P. Tilloch Ph. Mg. 62 



(1823) 168-, 244-, 348-, 433-. 

 --- . Buquoy, G. von. Oken Isis (1827) 



130-. 

 --- . Collins, E. St Pet. Ac. Sc. Mm. 1 



(1831) 583-. 

 --- . Novi, G. Tortolini A. 1 (1850) 



517-. 

 --- . Schlomilch, 0. Liouv. J. Mth. 8 



(1863) 99-. 



, general. Boole, G. Camb. and 

 Dubl. Mth. J. 3 (1848) 112-. 



--- into isotropic means. Cauchy, A. L. 



C. R. 34 (1852) 159- ; 43 (1856) 261-. 

 --- by substitution. Collins, E. [1826] 



St Pet. Ac. Sc. Mm. 1 (1831) 181-. 



and simplification, methods by interpolation. 

 Eichelmy, P. [1855] Tor. Mm. Ac. 17 (1858) 

 245-. 



Weierstrass's function, /(#) = S n & B cos (a n xir). 



Wiener, L. C. Crelle J. Mth. 90 (1881) 



221-. 

 z =f (x,y), graphic representation. Lalanne, L. 



Par. S. Phlm. PV. (1843) 71-. 

 f(x)f(x + l)...f(x + h), value. Gasparis, A. 



de. Nap. Rd. 1 (1852) 199-. 

 F(x, y), when a function of <f> (x, y), con- 



ditions. Dienger, J. Grunert Arch. 21 



(1853) 219-. 



fix), Wronski's expansion. Echols, W. H. 

 N. Y. Mth. S. Bll. 2 - 



178-. 



237 



