3250 Principles and Elements of the Integral Calculus 



Logarithmic integral J (log x)~* dx. Amstein, 



3250 



H. Laus. S. Vd. Bll. 31 (1895) 203- ; 36 



(1900) 1-. 



Mean area of rectangle with varying sides. 

 Breton [de Champ}, P. Liouv. J. Mth. 9 

 (1844) 373-. 



limits of two numbers. Ocagne, M. d'. 

 G. Teix. J. Sc. 7 (1886) 19-, 27. 



. Cesdro, E. G. Teix. J. Sc. 



7 (1886) 28-. 



value of function of several variables, 

 analytical determination. Philbert, H. 

 Liouv. J. Mth. 5 (1879) 115-. 



values. Hayes, E. Science 21 (1893) 333. 



, determination. Kronecker, L. C. E. 

 103 (1886) 980- . 



of functions of a real variable. Maurer, 



L. Mth. A. 47 (1896) 263-. 



theorem. Du Bois-Reymond, P. Crelle 

 J. 69 (1868) 65-. 



(Du Bois-Eeymond). Meyer, G. F. 



[1872] Mth. A. 6 (1873) 313-. 



, condition, new. Du Bois-Eeymond, 

 P. Mth. A. 7 (1874) 605-. 



for finite sums and integrals, second. 



Pringsheim, A. [1900] Munch. Ak. Sb. 30 



(1901) 209-. 



theorem, second. Mansion, P. Mathesis 



5 (1885) 97-. 



Periodic functions, theory based on integrals 

 between imaginary limits. Toeplitz, J. 

 Grunert Arch. 23 (1854) 241-. 



Points, distribution on a line. (Demonstration 

 of Peirce's propositions, Camb. (M.) Mth. M. 

 1 (1859) 16-18.) Adcock, R. J. Camb. (M.) 

 Mth. M. 1 (1859) 82-. 



r xdx 



Pseudoelliptic integral I , . Mar- 



kov, A. A. [1894/ StVet. Act Sc. Mm. 

 (Rs.) 75 (1895) 111-. 



Pyramid, triangular, Ixydm, I x' 2 dm, etc. 



Lobatto, R. Grunert Arch. 31 (1858) 249-. 

 Quadrature, approximate. Maggi, G. A. Ev. 



Mt. 3 (1893) 60-. 

 Quadratures, formula. Woolhouse, W. S. B. 



Assur. Mg. 13 (*1867) 119. 

 Eatio of two integrals taken between same 



limits. CebySev, P. [1882] St Pet. Ac. Sc. 



Mm. (Rs.) 44 (*1883) (Suppl.) No. 2, 33 pp. 

 Eational fractions. Cockle, (Sir) J. [1867] 



Mess. Mth. 4 (1868) 168-. 

 Eeduction formula. Mertens, F. Krk. Ak. 



(Mt.-Prz.) Ez. 8 (1895) 53-; Crc. Ac. Sc. Bll. 



(1893) 344. 

 . Gibson, G. A. Edinb. Mth. S. P. 14 



(1896) 27-. 



+ C n x 



dx. 



[C +C 1 x+C 2 x'i + 



, . Tikhomandritzky, . N. A. )r J (a - a)? (x - 



Schlomilch Z. 7 '(1862) 123-. 



Mth. 18 (1899) 173-. 

 , various orders. Schlomilch, 0. Leip. 



B. 10 (1858) 77-; Schlomilch Z. 3 (1858) 



301- . 

 Mechanical quadrature. Clausen, T. Crelle 



J. 6 (1830) 287-. 

 . Ligowski, W. [1875-76] Arch. Mth. 



Ps. 58 (1876) 49-; 59 (1876) 329-. 



. Vogel, R. Fschr. Mth. (1887) 283. 



. Lampe, E. [1893] D. Mth. Vr. Jbr. 



3 (1894) 102-. 

 . Poincare, H. Bll. As. 16 (1899) 382-. 



and interpolation. Grunert, J. A. 

 Grunert Arch. 20 (1853) 361-. 



, law of numerical coefficients. Oppolzer, 



T. von. As. Nr. 91 (1878) 329-. 

 , pairs of formulae in. Skutsch, R. Arch. 



Mth. Ps. 13 (1895) 78-. 



, Simpson's method. Hocevar, F. Wien 

 Ak. Sb. 90 (1885) (Ab. 2) 908-. 



, theory. Mehler, F. G. [1863] Crelle 



J. 63 (1864) 152-. 

 , . Gegenbauer, L. [1878] Wien Ak. 



Sb. 78 (1879) (Ab. 2) 768-. 

 , , generalisation. Stieltjes, . C. E. 



99 (1884) 850-. 



Minimum value of I ^ (dx^ + dx# + . . . + dx n 2 ) , 



the x's being connected by equation of second 



degree. Schldfli, L. [1849] Crelle J. 63 



(1852) 23-. ' 

 Numerical differential of a numerical integral. 



Tomashevlch, E. [1879] (xn) Eec. Mth. 



(Moscou) 9 (1878-81) (Pt. 1) 546-. 

 Partial fractions, extension of theorem relating 



to. Neumann, C. Gott. Nr. (1869) 9-. 



Spitzer, S. 



formulae. Moth, F. X. Baumgaftner Z. 

 6 (1829) 158-. 



. Winckler, A. Wien SB. 47 (1863) 

 (Ab. 2) 146-. 



. Watson, W. Mess. Mth. 3 (1866) 



Eelation of two integrals expanded to one and 



same value of variable. Chebuishev, P. L. 



(xn) Kazan S. Nt. (Ps.-Mth.) P. 1 (1883) 



pfe. 9] 43. 

 Eepresentative functions. Du Bois-Reymond, 



P. C. E. 92 (1881) 915-, 962-; Mth. A. 



18 (1881) 593-. 

 Eichard planimeter. Anon. Sc. Abs. 1 (1898) 



635. 

 Summation function. Kronecker, L. Berl. 



Ak. Sb. (1889) 867-. 

 Surface and volume integrals of ellipsoid, 



cases. Hogg, E. G. Aust. As. Ep. (1900) 



191-. 

 Symmetrical integrals, formula. Zucchetti, F. 



Tor. At. Ac. Sc. 4 (1868-69) 333-. 

 Theorem of Cebysev. Arone, G. d'. G. Mt. 



26 (1888) 61-. 

 . Cesdro, E. G. Mt. 27 (1889) 48-. 



Frullani, generalisation. Lerch, M. 

 Prag Sb. (1893) (Mth.-Nt.) No. 30, 6 pp. 



, geometrical. Beliankin, I. [1900] Eec. 

 Mth. (Moscou) 21 (1901) 461-. 



of Stokes. Fleuri, G. Aust. As. Ep. (1893) 

 297-. 



. Gosiewski,W. Wiad. Mt. 2 



213- ; Fschr. Mth. (1898) 247. 

 , generalisation. Maggi, G. A. Catania 



Ac. Gioen. At. 4 (1892) (Mm. 8) 12 pp. 



273 



