3210 



Theory of Functions of Real Variables 



3210 



Discontinuity, curious examples. Plateau, 

 J. A. F. Brux. Ac. Bll. 43 (1877) 84-, 

 255-. 



of functions, theorem. Casorati, F. Mil. 

 I. Lomb. Ed. 1 (1868) 123-. 



Discontinuous function. Lerch, M. G. Mt. 

 26 (1888) 375-. 



functions. Libri, G. Crelle J. 7 (1831) 

 224-; 10 (1833) 303-. 



. Boole, G. [1846] Ir. Ac. T. 21 (1848) 



124-. 



. Cauchy, A. L. C. E. 28 (1849) 277-. 



. Darboux, G. [1874] Par. EC. Norm. 



A. 4 (1875) 57- ; 8 (1879) 195-. 

 , application to analytic formulae. Libri, 



G. C. E. 15 (1842) 401-. 



connected with continuous. Baire, R. 

 C. E. 126 (1898) 1621-. 



developable by continuous. Baire, R. 



C. E. 126 (1898) 884-. 



, real, of real variable, analytical represen- 

 tation. Severini, C. Tor. Ac. Sc. At. 33 

 (1897) 762- or 1002- ; 34 (1898) 199-, 374- 

 or 325-, 518-. 



, representation. Rawson, R. [1846] 

 Manch. Ph. S. Mm. 8 (1848) 235-. 



, sum, theorem of Abel's. Catalan, E. C. 



Liege S. Sc. Mm. 15 (1888) No. 1, 153-. 

 , theorem, proof. Baire, R. Par. S. Mth. 



Bll. 28 (1900) 173-. 

 , theory. Piola, G. [1830] Mod. Mm. 



S. It. 20 (1828) 573-. 

 , . Haan, D. Bierens de. Amst. Vh. 



7 (1859) 52 pp. 

 , . Baire, R. C. E. 129 (1899) 



1010-. 

 and indeterminate functions. Wead, C. K. 



[1900] Wash. Ph. S. Bll. 14 (1906) 65-. 



punctuated functions. Volterra, V. G. Mt. 

 19 (1881) 76-. 



Double functions, changes. Decker, G. Grunert 



Arch. 21 (1853) 423- ; 27 (1856) 471-. 

 Elimination, a functional. Russell, W. H. L. 



Mess. Mth. 1 (1872) 102. 

 Empiric curves, deduction of true function 



from. Pucci, E. Em. E. Ac. Line. Mm. 6 



(1889) 316-. 



Functional powers. Collins, E. [1835] St Pet. 

 Ac. So. Mm. 3 (1838) 313-. 



problems. Abel, N. H. Mg. Ntvd. 1 (1823) 

 216- ; Grelle J. 2 (1827) 386-. 



. Decsy, S. (xn) Mag. Tud. Ak. Ets. 7 



(No. 6) (1873) 80-. 



symbols. Cayley, A. QJ. Mth. 4 (1861) 

 225-. 



Functions analogous to sine and cosine. 



Olivier, L. Crelle J. 2 (1827) 243-. 

 , application to pure geometry. Hoist, E. 



[1879] Par. S. Mth. Bll. 8 (1880) 52-. 

 , approximate representation, application 



of method of least squares. Schlomilch, O. 



Schlomilch Z. 3 (1858) 124-. 



dependent on lines. Volterra, V. Em. 

 E. Ac. Line. Ed. 3 (1887) (Sem. 2) 225-, 

 274-. 



determined by certain addition theorem. 

 Zignago, I. Em. N. Line. At. 53 (1900) 

 139-. 



, differentiate, with infinitely close (dicht) 

 maxima and minima. Broden, T. Stockh. 

 Ofv. (1900) 423-, 743-. 



expressible rationally in terms of one 

 another. Woepche, C. Liouv. J. Mth. 4 

 (1859) 339-. 



, having differential coefficient at every 

 point, and oscillating infinitely often in 

 every interval. Pereno, I. G. Mt. 35 (1897) 

 132-. 



no derivative throughout one interval. 



Dini, U. A. Mt. 8 (1877) 121-. 



not expansible by Taylor's theorem. 

 Pringsheim, A. Mth. A. 44 (1894) 41-. 



oscillating infinitely often, and discontinuous 

 functions. Hankel, H. Mth. A. 20 (1882) 

 63-. 



of real arguments, classification by changes 

 in least intervals. Du Bois-Reymond, P. 

 [1874] Crelle J. Mth. 79 (1875) 21-. 



one real variable. Burnside, W. Mess. 



Mth. 23 (1894) 39-. 

 . Somigliana, C. Em. E. Ac. 



Line. Ed. 8 (1899) (-Sem. 1) 4-, 618. 

 . Straneo, P. Em. E. Ac. 



Line. Ed. 8 (1899) (Sem. 1) 438-, 618. 



functions, differentiation. Runge, C. Z. , analytic representation. Weier- 



Mth. Ps. 42 (1897) 205-. strass, K. Berl. Ak. Sb. (1885) 633-, 



Evaluation of functions in indeterminate form. 789-. 



Unferdinger, F. Grunert Arch. 26 (1856) , . Mittag-Leffler, G. 



224-. Palermo Cir. Mt. Ed. 14 (1900) 217-. 



Finite and continuous functions having no with derivatives of every order. 



derivative. Dini, U. Em. E. Ac. Line. T. Maurer, L. Mth. A. 41 (1893) 377-. 



1 (1877) 70-, 130-. 



Fluctuating functions. Hamilton, (Sir) W. R. 

 [1840] Ir. Ac. T. 19 (1843) 264-. 



Fractional functions, decomposition and trans- 

 formation. Rangoni, L. [non Gabba, A.] 



and their differential coefficients. 



Harnack, A. Mth. A. 23 (1884) 244-; 24 



(1884) 217-. 

 , discontinuities. Bettazzi, R. 



Palermo Cir. Mt. Ed. 6 (1892) 173-. 

 , geometric mean value. 



Lemoyne, G. G. Mt. 16 (1878) 209-. 

 , special class. Study, E. Mth. 



A. 46 (1896) 298-. 



Brescia Cm. (1830) 150-. 



Function satisfying no algebraic functional equa- 

 tion. Holder, O. Gott. Nr. (1887) 662-. 



Functional analysis with application to paral- x , . 



lelogram of forces. Anon, (vi 553) Gergonne , theory. Echols, W. H. A. 



A. Mth. 14 (1823-24) 350-. Mth. 8 (1893-94) 65-. 



indices. Liventsov, A. L (xn) Eec. Mth. two real variables. Borel, E. Par. EC. 



(Moscou) 8 (1876) (Pt. 1) 277-. Norm. A. 13 (1896) 79-. 



236 



