6030 Functional Equations 



Functions determined by functional equation 

 in 2 variables. Vivanti, . Palermo Cir. 

 Mt. Ed. 4 (1890) 66-, 69. 



satisfying certain functional equations. 

 Wirtinger, W. Wien Ak. Sb. 99 (1891) (Ab. 

 2a) 918-. 



Generating functions. Rangoni, L. Mod. Mm. 



S. It. 19 (1821) 241-, 659-. 

 . Ostrogradsky, M. A. St Pet. Ac. Sc. 



Bll. 1 (1836) 73-. 

 and repeated differentiation. Jilrgensen, 



U. (vi Adds.) Kiob. Ov. (1830-31) 2-. 

 Integrals. Koenigs, G. C. B. 99 (1884) 1016- ; 



Par. EC. Norm. A. 1 (1884) (Suppl.) 41 pp. 

 Iteration and general algorithms. Lemeray, . 



Par. S. Mth. Bll. 26 (1898) 10-. 

 , problem. Lean, L. Par. S. Mth. Bll. 26 



(1898) 5-. 

 , , application of doubly periodic functions 



to solution. Lemeray, . Par. S. Mth. 



Bll. 27 (1899) 282-. 

 Iterations and reversion series. Zorawski, K. 



Krk. Ak. (Mt.-Prz.) Bz. 9 (1895) 240-; Ore. 



Ac. Sc. Bll. (1894) 242. 



Iterative and other functional equations, con- 

 ditions of holomorphism for integrals. 



Koenigs, G. C. B. 101 (1885) 1137-. 

 Lagrange-Foncenex lever problem. Genocchi, 



A. Tor. At. Ac. Sc. 4 (1868-69) 323-; 



Brux. Ac. Bll. 36 (1873) 181-. 

 Linear difference forms equivalent to their 



adjoints. Bortolotti, E. Bm. B. Ac. Line. 



Ed. 7 (1898) (Sem. 1) 257-, (Sew. 2) 46-. 

 Meaning of equation U^=V 2 , where U and V 



are products of linear functions. Kirkman, 



T. P. Camb. and Dubl. Mth. J. 5 (1850) 97-. 

 Eeduction of functional equations to finite 



difference equations. Herschel, (Sir) J. F. W. 



[1820] Camb. Ph. S. T. 1 (1822) 77-. 

 Bepeated functions. Tralles, J. G. Berl. Ab. 



(1814-15) (Mth.) 21 6-. 

 Beversion of series as connected with 

 \pa.- l ^ax = x. 



Homer, W. G. Thomson A. Ph. 11 (1818) 



108-. 

 Solution with conditions. Jensen, J. L, W. V. 



N. Ts. Mth. 8 (B) (1897) 25-; Fschr. Mth. 



(1897) 346. 



of a functional equation and application to 

 parallelogram of forces and to curves of 

 equilibration. Wallace, W. (Prof.) [1839] 

 Edinb. B.- S. T. 14 (1840) 625-. 



used by Poisson for parallelogram 



of forces. Perkins, G. R. Silliman J. 42 



(1842) 69-. 

 Symbolic equation, and its consequences. 



Pincherle, S. Bm. B. Ac. Line. Ed. 8 (1899) 



(Sem. 1) 152-. 



equations. Pincherle, S. Bologna Ac. Sc. 

 Mm. 5 (1895-96) 663-. 



Theory of functional equations. Bugaev, N. V. 



[1878] (xn) Bee. Mth. (Moscou) 9 (1878-81) 



(Ft. 1) 109-. 

 Transcendental functions, class. Winckler, A. 



Wien SB. 44 (Ab. 2) (1861) 477-. 

 Use of functional equations in elementary 



geometry. Sigma, (vi Adds.) Tilloch Ph. 



Mg. 65 (1825) 101-. 



Geometry 6400 



\f/ n x=x. Homer, W. G. Thomson A. Ph. 10 

 (1817) 341-. 



= . Herapath, J. Thomson A. Ph. 8 

 (1824) 420-. 



f{z,f(x, y)} symmetrical in x, y, z, determina- 

 tion. Abel, N. H. Crelle J. 1 (1826) 11-. 



<fi(fx) = <j>x (*?}. Ramus, C. Crelle J. 9 

 (1832) 359-. 



Sylvester, J. J. QJ. Mth. 3 (1860) 186-. 

 , coefficients consta 

 ologna Ac. Sc. Mm. 9 



"Lh v <t> (x + a v ) =f(x), coefficients constant. 



B 

 (1888) 45-. 



Pincherle, S. 



= , rational in x. Pincherle, S. Bo- 

 logna Ac. Sc. Mm. 9 (1888) 181-. 



GEOMETRY. 

 6390 General. 



Algorithms, geometry. Seguin, (aine) . 



Moigno An. Cosmos (1862) 451-. , 

 Equation of the beautiful. Lagout, E. Les 



Mondes 31 (1873) 480- . 

 Geometrical investigation, modern tendency. 



Segre, C. Ev. Mt. 1 (1891) 46-, 154-. 

 -- , -- (Segre). Peano, G. Ev. Mt. 1 



(1891) 66-, 156-. 



Geometry, linear and metric. Klein, F. [1871] 



Mth. A. 5 (1872) 257-. 

 Beductio ad absurdum, origin and avoidance. 



Hennessy, J. P. B. A. Ep. (1857) (pt. 2) 3. 



Foundations. 

 6400 General. 



Construction, geometrical, as proof of existence 

 in Greek mathematics. Zeuthen, H. G. N. 

 Ts. Mth. 3 (A) (1892) 105- ; Fschr. Mth. 



(1892) 48- ; Mth. A. 47 (1896) 222-. 

 Extension. Riccobelli, F. Brescia Cm. (1829) 



104-. 

 Functions, conception of, in teaching ele- 



mentary geometry. Besso, D. G. Mt. 7 



(1869) 131-. 

 Geometrical ideas, origins. Laquiere, E. M. 



As. Fr. C. B. (1881) 162-. 



intuition and analysis, connection. Schlofii, 

 L. Mil. I. Lomb. Bd. 5 (1872) 290-. 



-- , example. Monro, C. J. QJ. Mth. 2 



(1858) 225-. 

 Method in geometry. Tannery, J. Ens. Mth. 



1 (1899) 333-. 

 Morphology, analytic. Peirce, B. Am. As. P. 



(1855) 67-. 

 Perimeters and areas of circles, Legendre's 



demonstration. Breton [de Champ], P. N. 



A. Mth. 4 (1845) 415-. 

 Batio, principles of antecedental calculus. 



Glenie, J. [1794] Edinb. B. S. T. 4 (1798) 65-. 



412 



