1640 Calculus of Differences, etc. 



Finite differences calculus, formula in. Carr, 

 T. I. Act. J. 14 (* 1869) 479-. 



Malmsten, C. J. Stockh. Ak. Hndl. (1844) 



363-; Crelle J. 35 (1847) 55-. 

 --- , formulae. Tortolini, P. A. Mt. 5 



(1863) 181-. 

 --- , , useful. Hill, G. W. Des MMnes 



Anal. 1 (1874) 141-. 

 --- , methods. Carmichael, R. NH. Ev. 



7 (1360) (P.) 78-, 170-. 

 --- -, theorem, new. Booth, J. Ph. Mg. 



19 (1841) 125-. 



, theorems, new, based chiefly on re- 



searches on complex variability. Casorati, F. 



A. Mt. 10 (1880-82) 10-. 

 -- , and theory of numbers, contribution 



to. Busche, E. Mth. A. 53 (1900) 243-. 

 -- , direct method. Adams, Jas. Thomson 



A. Ph. 16 (1820) 281-. 

 -- , formula. Cayley, A. QJ. Mth. 2 (1858) 



198-. 

 -- , formulae. Cauchy, A. L. C. E. 19 



(1344) 1179-. 

 -- , integrals. Cauchy, A. L. C. E. 39 



(1854) 21 i-. 

 -- , . Bmmiakowtky, V. St Pet. Ac. Sc. 



Mm. 1 (1859) No. 9, 13 pp. 

 , E. Les 

 701-. 



-- , . Barbier, 



Mondes 3 (1863) 



-- , . Thoman,F. C. E. 57 (1863) 778-. 

 -- of powers, conversion to definite integrals. 



Cauchy, A. L. [1815] Par. EC. Pol. J. 17 



(28 cah.) (1841) 147-. 

 -- , return to original series from nth term of 



with series of differences. Mtiller, G. W. 



Grunert Arch. 1 (1341) 211-. 



, series connected with. Lukas, F. C. 

 Wien Az. 32 (1395) 269-. 



-- , and Taylor's series. Carvallo, E. N. A. 

 Mth. 10 (1391) 24-. 



or mixed differences, uestions depending 

 on. Combescure, E. Par. EC. Norm. A. 

 3 (1874) 305-. 



Forms A" O x and congeners. Horner, J. QJ. 



Mth. 4 (1861) 111-, 204-. 

 Formula for A0 i / i when and i are very large 



numbers. Cayley, A. [1387] Edinb. E. S. P. 



li (1388) 119-. 

 Functions, approximate forms for representa- 



tion. Pincherle, S. Bologna Ac. Sc. Mm. 



10 (1889) 77-. 

 Harmonic series, representation by sequences 



of factors. Eogel, F. Arch. Mth. Ps. 9 



(1890) 297-. 

 Illusory interpolations, new examples. Meray, 



C. Ell. Sc. Mih. 20 (1396) 266-. 

 Indeterminate analysis, application of calculus 



of finite differences. Piola, G. A. Sc. Lomb. 



Ven. 1 (1831) 101- ; Tortolini A. 1 (1350) 263-. 

 Integrability of differential and finite difference 



equations, conditions. Mmich, S. R. Tor- 



tolini A. 1 (1350) 321-. 

 Integral, finite, 2 n #a; expressed as a definite 



integral. Abel, N. H. Mg. Ntvd. 6 (1325) 



182-. 



Interpolation 1640 



Integral, finite, 2e*7/. Malmsten, C. J. Ups. 



N. Acta S. Sc. 12 (1844) 293-. 

 Integration of difference equations reducible to 



linear form. Oltramare, G. As. Fr. C. E. 



(1893) (Pt. 2) 106-. 



in finite differences. Trembley, J. Berl. 

 Mm. Ac. (1799-1300) 18-. 



of linear difference-equations. Oltramare, G. 

 As. Fr. C. E. (1891) (Pt. 2) 66-; (1895) 

 (Pt. 2) 175-. 



, use in arithmetical calculations. Cesdro, 

 E. Palermo Cir. Mt. Ed. 1 (1387) 293-. 



Interpolated multiples. Soule, . Bordeaux 

 S. Sc. Mm. 4 (1894) iii-. 



Interpolating functions. Cauchy, A. L. C. E. 

 11 (1840) 775-. 



. Genocchi, A. Tor. Ac. Sc. At. 13 



(1877) 716- ; 15 (1880) 269-; C. E. 86 



(1878) 466-. 



. Peano, G. Tor. Ac. Sc. At. 18 (1882) 



573-. 



, elementary proof of a fundamental 

 property. Schwarz, C. H. A. Tor. Ac. Sc. 

 At. 17 (1381) 740-. 



INTEEPOLATION. 



Legendre, A. M. Con. des Temps (1819) 



302-. 



Degen, C. F. As. Nr. 1 (1823) 231-. 

 Clausen, T. Crelle J. 5 (1829) 305-. 

 Encke, J. F. Berl. As. Jb. (1830) 265-. 

 Cauchy, A. L. [1835] Mod. Mm. S. It. 21 



(1836) 374-. 



Biot, J. B. C. E. 13 (1344) 545. 

 Brassinne, E. Liouv. J. Mth. 11 (1846) 



177-. 

 Cauchy, A. L. Con. des Temps (1852) 129- ; 



C. E. 37 (1853) 64-. 



Lehmann, J. W. H. As. Nr. 39 (1855) 257-. 

 Grunert, J. A. Grunert Arch. 32 (1859) H9-. 

 Hermite, C. C. E. 48 (1359) 62-. 

 Rouche, E. N. A. Mth. 13 (1859) 26-. 

 Cebysev, P. St Pet. Ac. Sc. Mn. (Rs.) 4 



(* 1864) (Suppl.) No. 5, 23 pp. 

 Tisserand, F. C. E. 68 (1869) 1101-. 

 Nell, A. M. Arch. Mth. Ps. 61 (1877) 135-. 

 Bartl, C. [1877] Arch. Mth. Ps. 62 (1378) 



202-. 

 Laisant, C. A. As. Fr. C. E. (1891) (Pt. 2) 



222-. 

 Pincherle, S. Bologna Ac. Sc. Maa. 3 (1392) 



293-. 



Borel, E. C. E. 124 (1397) 673-. 

 Laisant, . As. Fr. C. E. (1897) (Pt. 2) 86-. 

 Markov, A. St Pet. Ac. Sc. Mm. 6 (1398) 



No. 5, 69 pp. ; Fschr. Mih. (1898) 252-. 

 Veltmann, W. Z. Mth. Ps. 44 (1899) 303- ; 45 



(1900) 337. 

 and application to cubic equations. Vieille, J. 



N. A. Mth. 10 (1851) 48-. 

 applied to extraction of square and cube roots. 



Dolguschin, P. A. Fschr. Mth. (1898) 139. 

 approximate. Bellavitis, G. Ven. At. (1858- 



59) 1109-. 

 fractions. Gyory, S. (xn) Mag. Ak. Ets. 



(1854) 165-. 



123 



