6030 



Solution, general, of equations, 1st order. 

 Kramp, C. Erfurt N. Acta 1 (1799) 71-. 



of linear differential and difference equa- 

 tions by definite integrals. Brajtzew, J. R. 

 Fschr. Mth. (1900) 356. 



or difference equations in series. 



Pincherle, S. Palermo Cir. Mt. Ed. 2 (1888) 

 153-. 



equation in most general form. 

 t Sylvester, J. J. B. A. Ep. (1862) (pt. 2) 



188. 



equations. Hargreave, C. J. [1849] 



Phil. Trans. (1850) 261-. 



of finite and mixed differences. 

 Gregory, D. F. Camb. Mth. J. 1 (1839) 

 54-. 



with variable coefficients. Zehfuss, 



G. Schlomilch Z. 3 (1858) 175-. 



G(x + l)-G(x) = H (x) . Guichard, C. 



Par. EC. Norm. A. 4 (1887) 361-. 



n sA 2 a n * n = "2^^. Lerch, M. 6a- 



n=f> n=2 n 



sopis 21 (1892) 69-; Fschr. Mth. (1892) 



317-. 



Solutions, conjugate, in differential and differ- 

 ence equations. Pincherle, S. Em. E. Ac. 



Line. Ed. 4 (1895) (Sem. 2) 228-. 

 , particular. Poisson, S. D. Par. EC. Pol. 



J. 13" cah. (1806) 60-. 

 , rational, of 



C$ (n) f tn + 1) + (A n " + B") $ (n + 1) 



- (A' ( + 1) +B') t (n) + (A' - A") =0. 



Saalschiitz, L. Crelle J. Mth. 119 (1898) 



291-. 

 , singular. Brunacci, V. [1808] Mod. Mm. 



S. It. 14 (1809) 175-. 

 $*x, i-e. <(>-if z <t>x. Horner, W. G. Thomson 



A. Ph. 11 (1826) 168-, 241-. 

 P n+1 = nP n + P n _ 1 . Catalan, E. C. Liege S. 



Sc. Mm. 15 (1888) No. 1, 235-. 



6030 Solution of functional equa- 

 tions. (See also 4460.) 



Bdbbage, C. Gergonne A. Mth. 12 (1821-22) 



Herap'ath, J. Tilloch Ph. Mg. 64 (1824) 197-, 



333-; 66 (1825) 102- ; 67 (1826) 442-. 

 Ellis, JR. L. Camb. Mth. J. 3 (1843) 131-. 

 Schlomilch, 0. Leip. B. (1852) 27-. 

 Koenigs, G. Par. EC. Norm. A. 2 (1885) 385-. 

 Grevy, A. fill. Sc. Mth. 16 (1892) 311- ; Par. 



EC. Norm. A. 11 (1894) 249-; 13 (1896) 



295-. 

 Leau, . C. E. 119 (1894) 901- ; 120 (1895) 



427-. 

 Pexider, J. V. fiasopis 29 (1900) 153- ; Fschr. 



Mth. (1900) 403. 

 Algebraic and functional equations, distinction. 



Ettit, E. L. Camb. Mth. J. 3 (1843) 92-. 

 functional equations and linear differential 



equations, irreducibility. Koenigsberger, L. 



Mth. A. 53 (1900) 49-. 

 Algorithm, new. Ldmeray, . C. E. 125 



(1897) 524-. 



Solution of Functional Equations. 



6030 



Cases. Gregory, D. F. Camb. Mth. J. 3 (1843) 

 239-. 



. Ellis, R. L. Camb. and Dubl. Mth. J. 7 

 (1852) 103-. 



. Cayley, A. QJ. Mth. 15 (1878) 315-, 

 338-. 



. Jezek, 0. Prag Sb. (1885) (Mth.-Nt.) 

 63-. 



. Croftan, M. W. [1888] Ir. Ac. P. 1 (1889- 

 91) 20-. 



. Giudice, F. Palermo Cir. Mt. Ed. 2 

 (1888) 28-. 



. Lecornu, L. Par. S. Mth. Bll. 23 (1895) 

 102-. 



. Nielsen, N. Kjtfb. Ov. (1897) 185- ; Fschr. 

 Mth. (1897) 346-. 



. Zejliger, D. N, [1900] Kazan S. Ps.- 

 Mth. Bll. 10 (1901) 187-. 



Closed systems of operations. Brunei, . 



Bordeaux S. Sc. Mm. 5^1890) x-. 

 Convergent iterations. Zorawski, K. Krk. 



Ak. (Mt.-Prz.) Ez. 6 (1893) 271- ; Crc. Ac. 



Sc. Bll. (1893) 144-. 

 Equation, fundamental, of Thiele's. Steen, A. 



(xn) Ts. Mth. 4 (1868) 129- ; 5 (1869) 26-. 

 Expansion in series of repeated index function 



(4th ' ' Eechnungsstuf e ") . Paugger, F. Gru- 



nert Arch. 35 (1860) 21-. 

 To find f(x) from equations / (x + y) =f (x) 



/(?/), f(x + y)=f(x) .f(y) by elementary 

 means. Jensen, J. L. 

 2 (1878) 149-. 



W. V. (xn) Ts. Mth. 



Form of function satisfying equation 



F(x + z)+F(x-z)=aF(x) . F (z). 



Holmboe, B. M. Mg. Ntvd. 1 (1832 ?) 275-. 

 Formation of equations satisfied by given alge- 



braic functions. Tortolini, B. [1848] Bo- 



logna N. Cm. 9 (1849) 283-. 

 Functional equation of Poisson. Andrade, . 



Par. S. Mth. Bll. 28 (1900) 58-. 



Mainardi, G. Tortolini A. 4 (1853) 331-. 

 -- treated by Abel. Stiickel, P. Z. Mth. 

 Ps. 42 (1897) 323-. 



equations characterising associative and 

 distributive operations. Lemeray, . Par. 

 S. Mth. Bll. 27 (1899) 130-. 



-- with 2nd member. Grevy, . Par. S. 

 Mth. Bll. 25 (1897) 57-. 



, principle defective. Herschel, (Sir) 

 J. F. W. Camb. Mm. Anal. S. (1813) 65-. 



with 1 or more variables. Leau, L. 

 Toul. Fac. Sc. A. 11 (1897) E, 110 pp. 



linear equations. Lemeray, . C. E. 125 

 (1897) 1160- ; 126 (1898) 949- ; As. Fr. C. E. 

 (1900) (Pt. 2) 208-. 



relation of 2 variables x, y. Roselli, E. 

 G. Arcad. 115 (1848) 129-. 



Functions, calculus. Russell, W. H. L. Phil. 

 Trans. (1862) 265-. 



determined by functional equation in 2 

 variables. Giudice, F. Palermo Cir. Mt. 

 Ed. 2 (1888) 28-, 94-; 3 (1889) 273-; 4 

 (1890) 67-. 



-------- . Peano, . Palermo 



Cir. Mt. Ed. 2 (1888) 94, 187-. 



411 



