6000 



Functional and Difference Equations 



6020 



Problem of hydrodynamics, Dirichlet's. Brios- 

 chi, F. [1860] Crelle J. 59 (1861) 63-. 



Eesidual integral in -=a 2 V 2 u. Hadamard, 



. Par. S. Mth. Bll. 28 (1900) 69-. 

 Solution of Laplace's equation, finite and con- 

 tinuous with normal deviation given at all 



points of bounding surface. Stekloic, W. A. 



Fschr. Mth. (1897) 364-. 

 Steady flow of electricity on rectangular plate. 



Mathieu, E. As. Fr. C. E. (1886) (Pt. 2) 1-. 

 Stokes's theorem for hydrokinetic circulation, 



proof. Mukhopadhyay , A. Beng. As. S. J. 



59 (Pt. 2) (1891) 59-. 

 Theorem of Picard. Kobb, G. C. E. Ill (1890) 



726-. 

 Poincare. Zaremba, S. C. E. 127 (1898) 



215-. 

 Thermal equilibrium of closed radiating surface. 



Picard, E. C. E. 130 (1900) 1499-. 

 Values on closed surface, determination of 



integrals of partial non-linear equations by. 



Le Roy, E. C. E. 124 (1897) 1508-. 

 Vaschy's theorem on any vectorial distribution. 



Larose, . Par. S. Mth. Bll. 24 (1896) 



177- % 



-- + ( -^ = Q. Liouville, J. Liouv. J. Mth. 

 dx* dy- 



8 (1843) 265-. 

 V 2 u = e u . Picard, E. Liouv. J. Mth. 4 (1898) 



313-. 



Difference equations and functional 

 equations. 



6000 General. 



Analytic factorials, reduction in series. Novi, 



G. G. Mt. 2 (1864) 1-, 40-. 

 Difference equation, 2nd order. Cayley, A. 



QJ. Mth. 14 (1877) 23-. 

 Differential coefficients, calculation from tables. 



Sheppard, W. F. Nt. 60 (1899) 390-. 

 and finite differences. Makeham, W. M. 



I. Act. J. 16 (* 1872) 98-. 



equations, numerical solution. Ldska, W. 

 Prag Sb. (1897) (Mth.-Nt.) No. 35, 10 pp. 



Euler' s formula, deduction. Zbikovskij, A. 

 [1870] St Pet. Ac. Sc. Mm. (Rs.) 18 (*1871) 



Finite differences. Lobatto, R. Amst. N. Vh. 

 6 (1837) 1-. 



increments, generalisation of formula for. 

 Stieltjes, T. J. N. A. Mth. 7 (1888) 26-. 



Generic equations, class. Blissard, J. QJ. 



Mth. 5 (1862) 325-. 

 Interpolation formula. Roe, E. D. [1900] N. 



Y. Am. Mth. S. Bll. 7 (1901) 202, 203-. 

 Lagrange's calculus of functions, superiority 



to infinitesimal calculus. Magistrini, G. B. 



[1832] Bologna Mm. Ac. Sc. 1 (1850) 93-. 

 Linear difference forms, algebra. Pincherle, S. 



Bologna Ac. Sc. Mm. 5 (1895-96) 87-. 

 Numbers, A m O n class, properties. Blissard, J. 



QJ. Mth. 8 (1867) 85-; 9 (1868) 82-, 154-. 



Numbers, < = [> - (f ) (p - 1)-+ ... 



Ocagne, M. d'. G. Teix. J. Sc. 8 (1887) 



171- ; 10 (1891) 185-. 

 Progressions. Jadanza, N. G. Mt. 7 (1869) 



117-. 

 Eecurring systems of 3rd order, especially 



periodic systems. Bortolotti, E. Palermo 



Cir. Mt. Ed. 5 (1891) 129-. 

 Sum of functions of quantities in arithmetical 



progression. Richmond, H. W. Mess. Mth. 



21 (1892) 29-. 

 Summation formula of Euler. Enestrom, G. 



Stockh. Ofv. 36 (1879) No. 10, 3-. 

 -- Stirling. Sonin, N. Ja. [1889] Vars. 



S. Nt. Tr. (1889-90) (C. R., Ps. C.) No. 2, 1-. 



formulas of Euler and Stirling. Sonin, N. 

 Ja. [1889] Vars. S. Nt. Tr. (1889-90) (C. R., 

 Ps. C.) No. 1, 2-. 



-- in finite differences. Glaisher, J.W. L. 

 QJ. Mth. 29 (1898) 303-. 



6020 Solution of equations of 

 finite differences. 



Murphy, R. [1835] Camb. Ph. S. T. 6 (1838) 91-. 

 Ellis, R. L. Camb. Mth. J. 4 (1845) 182-. 

 Siverly, W. Des Moines Anal. 1 (1874) 8-. 

 Pincherle, S. Em. E. Ac. Line. Ed. 3 (1894) 



(Sem. 1) 12-, 99-. 

 Case. Catalan, E. C. Liouv. J. Mth. 3 (1838) 



508- ; 4 (1839) 95-. 



. Walton, W. [1867] QJ. Mth. 9 (1868) 108-. 



. Sylvester, J. J. Ph. Mg. 8 (1879) 120-. 

 Class of equations of integrable form. Syl- 



vester, J. J. C. E. 54 (1862) 129-, 170-. 

 Difference and differential equations, con- 



nexion between. Mellin, H. Acta Mth. 9 



(1887) 137-. 

 ---- , of integrals. Tartolini, B. G. 



Arcad. 97 (1843) 45-. 

 ---- , integrable class. Sylvester, J. J. 



[1881] (xn) J. H. Un. Cir. [1] (1882) 178. 

 --- , law of reciprocity. Spitzer, S. 



Grunert Arch. 33 (1859) 415-. 



Equation connected with ^ (e~*). Vivanti, G. 



G. Teix. J. Sc. 11 (1892) 167-. 



, 2nd order. Sylvester, J. J. Ph. Mg. 37 

 (1869) 225-. 



__, __ , general. Muir, T. Ph. Mg. 17 

 (1884) 115-. 



of nth order has n constants in its solution. 

 Enestram, G. Stockh. Ofv. (1886) 247-; 

 Fschr. Mth. (1886) 303-. 



Equations for approximating to differential 

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

 (1837) 230-. 



, 1st degree, in 1 variable. Herschel, (Sir) 

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



of mixed differences. Biot, J. B. [1799] 

 Par. S. Phlm. Bll. 2 (1799-1801) 86-; Par. 

 Mm. Sav. Etr. 1 (1806) 296-. 



409 



