3250 Principles and Elements of the Integral Calculus 



Wronski's theorem. Transon, A. E. L. N. A. 



Mth. 13 (1874) 305- ; Par. T. Nauk Sc. 



Pam. 8 (*1876) Art. 8, 8 pp. 

 , Cayley ' s demonstration . Transon, A.E.L. 



N. A. Mth. 13 (1874) 161-. 

 , demonstration. Zurakowski, S. Krk. 



Ak. (Mt.-Prz.) Pam. 14 (1888) 56-; Fschr. 



Mth. (1888) 250. 

 F(x)+f(x + h)-f(x) _ F(x) + hf'(x + 6h) 



3250 



FI () +/i (x + h) -/i (*) F l (x) + hft (x + eh) ' 



where < < 1. Arez, J. G. Teix. J. Sc. 



11 (1892) 187- ; Fschr. Mth. (1893-94) 463. 



/ (e ax ) . general term of series for. Petrovitch, M. 



Palermo Cir. Mt. Ed. 14 (1900) 22-. 



3250 Principles and elements of 

 the integral calculus. Approxi- 

 mate integration. Mechanical 

 quadrature. 



Algebraic integrals. Nicolai, F. B. G. As. Nr. 



5 (1827) 376- ; 6 (1828) 79-. 

 of algebraic differentials, determination. 



Zeuthen, H. G. C. E. 90 (1880) 1114-. 

 Amsler's planimeter, theory. Thire, A. A. 



Mines 11 (1887) 121-. 

 Analysis, formula. Bassani, A. G. Mt. 25 



(1887) 225-. 

 , formulfe, two. Bruno de Cabedo, J. G. Teix. 



J. Sc. 9 (1889) 129- ; Fschr. Mth. (1889) 234. 

 Approximate calculation of integrals of higher 



orders. Bellavitis, G. (vi Adds.) Ven. Mm. 



I. 6 (1856) 91-. 



formula for measurement of area. Petit- 

 Bois, G. Ev. Un. Mines 27 (1894) 135-. 



value of area of segment of curve. Hermite, . 



Kazan S. Ps.-Mth. Bll. 8 (1899) 109. 

 Approximation formula. Thiele, T. N. (xn) 



Ts. Mth. 3 (1873) 22-. 

 Asymptotic functions. Sonin, N. Ja. [1889] 



Vars. S. Nt. Tr. (1889-90) (G. R., Ps. C.) 



No. 3, 1-. 

 Change of variables. Gauchy, A. L. C. E. 



23 (1846) 382-. 

 in calculation of integrals. Saltel, L. 



[1881] Bordeaux S. Sc. Mm. 4 (1882) 451-. 

 integrals. Schlomilch, 0. Grunert 



Arch. 18 (1852) 391-. 

 Convergence of integrals with non-vanishing 



arguments. Du Bois-Reymond, P. [1877] 



Mth. A. 13 (1878) 251-. 

 Differential equation for Milner's lamp. Tait, 



P. G. Edinb. Mth. S. P. 5 (1887) 97-. 

 . Cayley, A. Edinb. Mth. S. 



P. 5 (1887) 99-. 



and integral calculus, notations. J., J. 

 Ph. Mg. 24 (1844) 25-. 



Differentiation of integral with respect to upper 

 limit. Thomae, J. Gott. Nr. (1893) 696-. 



and integration of real function with one 

 independent variable. Gosiewski, W. Par. 

 T. Nauk Sc. Pam. 12 (*1882) Art. 3, 15 pp. 



, repeated, under sign of integration. Schlo- 



Differentiation under sign of integration. 



Werner, 0. Grunert Arch. 18 (1852) 39-. 

 ----- . Kapteyn, W. N. Arch. Wisk. 



4 (1899) 245-. 

 Difficult integrals. Euler, L. [1780] St Pet. 



Ac. Sc. Mm. 6 (1818) 30-. 

 soluble by other means. Euler, L. 



[1777] St Pet. Ac. Sc. N. Acta 14 (1805) 



62-. 

 Discontinuous function (x) and applications. 



Sonin, N. Ja. Vars. S. Nt. Tr. (Mm.) 1 



(1891) No. 5, 78 pp. 

 Distributive operations ; successive integration. 



Pincherle, S. Em. E. Ac. Line. Ed. 5 (1896) 



(Sem. 1) 236-. 

 Euler's "Integral Calculus," problems in. 



Goutinho; R. de S. [1806] Turin Mm. Ac. 



2 (1805-08) 95-. 



" -- ." Vol. iv, Suppl. 4, Sec. 2. Farini, 

 G. Padova N. Sag. 2 (1825) 249-. 



Exponential integral ^ . Wolfers, J. P. 



Grunert Arch. 20 (1853) 247-. 



-- (Wolfers). Lindman, C. F. Grunert 

 Arch. 23 (1854) 445-. 



Expressions, integrals of which are algebraic. 



Liouville, J. [1832-37] Par. EC. Pol. J. 



22 cah. (1833) 124-, 149- ; Crelle J. 10 



(1833) 347-; C. E. 5 (1837) 330-. 

 Farm, mean distance from farm yard. Was- 



mund, G. Grunert Arch. 13 (1849) 96-. 

 Finite integral of rational algebraic function. 



Orchard, W. Assur. Mg. [1 (*1861)] 9 (bis)-. 

 Formula, Brinkley's, for Lagrange's summa- 



tion. Herschel, (Sir) J. F. W. Phil. Trans. 



(1860) 319-. 



of Euler, 



milch, 0. Z. Mth. Ps. 15 (1870) 207-. 



Rodrigues, J. M. G. Teix. J. Sc. 3 (1881) 



157-. 

 , general, of Cauchy. Kapteyn, W. Bll. Sc. 



Mth. 16 (1892) 270-. 

 Fresnel's integrals, theory. Lindstedt, A. 



A. Ps. C. 17 (1882) 720-. 

 Functional relation 



u = x sin x + cos x} 

 v = sin x - x cos x] ' 



Strekalov, V. Kazan S. Ps.-Mth. Bll. 3 



(1893) (Prot.) 58-. 

 --- . Zejliger, D. Kazan S. Ps.-Mth. 



Bll. 3 (1893) (Prot.) 64-. 

 Functions, first derivative of which is of zero 



class. Ascoli, G. Mil. I. Lomb. Ed. 12 



(1879) 337-. 

 Hohmann-Coradi integrator. Reitz, F. H. 



Hamb. Mth. Gs. Mt. 1 (1889) 48-. 

 Integrability in finite form of 



Ptaszycki, . Bll. Sc. Mth. 12 (1888) 262-. 

 of functions. Peano, G. [1883] Tor. Ac. 

 Sc. At. 18 (1882) 439-. 



267 



