Calculus of Differences ; Interpolation 



1640 



Boole's finite differences, notation. Wilding, E. 



I. Act. J. 22 (*1881) 60-. 

 Calculus of differences, algebraic transformation 



by. Cesdro, E. N. A. Mth. 5 (1886) 489-. 

 , finite and infinitesimal. Gregory, 



D. F. Camb. Mth. J. 1 (1339) 212-. 

 , point in. Tisserand, F. C. E. 70 



(1870) 678-. 

 , theorem. Hamilton, (Sir) W. E. 



B. A. Ep. (1843) (pt. 2) 2-. 



enlargement (extension of calculus of 

 finite differences). MeClintock, E. Am. J. 

 Mth. 2 (1879) 101 -. 



, theorems. MeClintock, E. Am. J. 



Mth. 17 (1895) 69-. 

 functions derived from limiting ratios. 



Echols, W. H. [1395] A. Mth. 10 (1895-96) 



50-. 

 generating functions. L., E. J. Camb. 



Mth. J. 2 (1841) 94-. 

 Central-difference formulas. Sheppard, W. F. 



[1399] L. Mth. S. P. 31 (1900) 449-. 

 interpolation formula* Everett, J. D. 



B. A. Ep. (1900) 648-. 



formulas. Spencer, J. I. Act. J. 

 33 (1898) 349-. 



Constant coefficients in finite differences, theory. 



Naylor, J. I. Act. J. 23 (*1382) 420-. 

 Convergents applied to Cauchy's interpolation 



fractions. Pade, H. C. E. 130 (1900) 697-. 

 Cotes' numbers, calculation by approximate 



quadratures. Blazek, G. Prag Sb. (1879) 



167-. 

 Cotton spinning problem. Woolhouse, W. S. B. 



Assur. Mg. 11 (*1364) 224-. 

 Cyclical equations, connection with method of 



least squares. Nekrasov, P. A. Eec. Mth. 



(Moscou) 12 (1385) 377-. 

 Deduction of increase rates from tables. Everett, 



J. D. Nt. 60 (1899) 271. 

 . Eunge, C. Nt. 60 (1399) 



365-. 

 A m O n applied to integration. Herapath, J. 



Tilloch Ph. Mg. 65 (1325) 321-. 

 and Hargreave's form of it. Sums of 



powers of numbers etc. Scott, G. [1865] 



QJ. Mth. 8 (1867) 21-. 

 Determination of functions from special values 



of variable. Chebuishev, P. L. (xn) [1369] 



Eec. Mth. (Moscou) 4 (1369-70) (Pt. 1) 231-. 

 Difference, ith, deduced from nth differential. 



Picart, A. N. A. Mth. 12 (1373) 413-. 

 Differences and differential coefficients, con- 

 nexion between. Nielsen, H. P. N. Ts. 



Mth. 8 (B) (1397) 86-; Fschr. Mth. (1897)246. 

 differentials of functions of zero. Hamilton, 



(Sir) W. E. [1831] Ir. Ac. T. 17 (1337) 235-. 

 nth order. Spitzer, S. Grunert 



Arch. 33 (1359) 115-. 



method, application to series summed by 

 help of impossible quantities. Gompertz, B. 

 Phil. Trans. (1806) 174-. 



, construction of tables by. Gray, P. 



Assur. M ? . 13 (*1367) 61-, 149-, 293-; I. 



Act. J. 14 (*1869) 307-. 

 , , 2 theorems. Knight, T. Phil. Trans. 



(1317) 234-. 

 ,mth,ofO. Scott, G. QJ. Mth. 5 (1362) 323-. 



1640 



Differences, relation between various orders. 



Harvey, G. Thomson A. Ph. 7 (1816) 475-. 

 , series of, theory. Werner, 0. Grunert 



Arch. 23 (1354) 231- ; 24 (1855) 90-. 

 , , . Wallentin, I. G. Arch. Mth. 



Ps. 63 (1879) 56-. 



and Taylor's theorem. Adams, Jas. Thom- 

 son A. Ph. 11 (1818) 275. 



, theory. Sharpe, S. Ph. Mg. 19 (1831) 137-. 



of 0. Alberti, V. G. Mt. 38 (1900) 11 1-. 

 Differentiation by aid of finite differences and 



vice-versa. Lobatto, E. Crelle J. 16 (1837) 

 11-. 



, arithmetical. Philippoic, M. M. Fschr. 

 Mth. (1899) 267. 



under sign of integration, extension to finite 

 differences, with applications. Chio, F. Tor. 

 At. Ac. Sc. 6 (1870-71) 194-. 



Empirical formulae. Kleiber, I. A. Es. Ps.-C. 



S. J. 22 (Ps.) (1890) 11-; J. de Ps. 10 (1891) 



433-. 

 , comparison. Runge, C. Z. Mbh. Ps. 



45 (1900) 78-. 

 Equation of finite differences, giving sums and 



differences of Ex. Gaudin, (Col.) . Les 



Mondes 3 (1863) 567-. 

 Equations, algebraic, theorems. Mathieu, E. 



N. A. Mth. 15 (1856) 409-. 



of differences for approximating to differential 

 equation. Coriolis, G. Liouv. J. Mih. 2 

 (1837) 230-. 



Error of linear interpolation. Bary, . Ger- 



gonne A. Mih. 21 (1830-31) 281-. 

 Errors by interpolation from logarithmic and 



other tables. Woodward, E. S. A. Mth. 2 



(1885-86) 54-. 

 , logarithmic. Howe, H. A. A. Mth. 1 



(1884-85) 126- ; 2 (1885-86) 39-, 77-; 3 



(1887) 74. 

 , theory, formula in. Makeham, W. M. 



I. Act. J. 28 (1890) 393-. 

 Euler's summation formula. Landre, C. L. 



N. Arch. Wisk. 6 (*1880) 212-. 

 Exponential functions and finite differences. 



Herschel, (Sir) J. F. W. [1815] Phil. Trans. 



(1816) 25-. 

 Factorial notation. Elphinstone, H. W. QJ. 



Mth. 2 (1858) 122-, 254-. 

 Faculties expressed by A m O n . Jeffery, H. M. 



QJ. Mth. 4 (1861) 364-. 

 Figurate numbers and interpolation, short proofs 



of theorems. Soufflet, . Les Mandes 13 



(1867) 336-. 



series. Smyth, B. B. Kan. Ac. Sc. T. 14 

 (1896) 29-. 



Finite difference equations, partial. Paoli, P. 



Mod. S. It. Mm. 8 (1794) 575-. 

 integrals expressed by definite integrals. 



Tortolini, B. Tortolini A. 4 (1853) 209-. 



differences calculus. Eussell, W. H. L. 

 M3ss. Mth. 11 (1882) 33-. 



applied to definite integrals. Paoli, P. 



Mod. S. It. Mm. 20 (1828) 255-. 

 , A n (x m ), factor in general term of. 



Kohlau, E. Crelle J. 6 (1830) 255-. 

 , determinants of functions in the. 



Bortolotti, E. Em. E. Ac. Line. Ed. 5 (1896) 



(Sem. 1) 254-. 



122 



