3260 Definite Integrals (simple) 



Definite integrals involving exponential integral. 

 Glaisher, J. W. L. QJ. Mth. 18 (1882) 370-. 



in mechanics of motion of point on 

 surface. Rouche, E. Liouv. J. Mth. 3 (1858) 

 337-. 



obtained by symbolic methods. Bromvin, 



B. Camb. and Dubl. Mth. J. 3 (1848) 243-. 

 with periodic factor. Chartier, J. Liouv. 



J. Mth. 18 (1853) 201-. 



in planetary motion, numerical expression. 



Lefort, F. Liouv. J. Mth. 11 (1846) 142-. 



of products of functions, inequalities 

 limiting value of. Imshenetskii , V. G. (xn) 

 Kharhov Mth. S. Com. (1882) 99-. 



, relation between. Andreief, 



C. Bordeaux S. Sc. Mm. 2 (1886) 1-. 

 . , theorems of Cebysev and 



Imseneckij. Andreev,K.A. (xn) Kharkov 

 Mth. S. Com. (1882) 110-. 



[ve~ x dx 



reducible to 



Arndt, F. Grunert Arch. 10 (1847) 233-. 



representing functional operations. 

 Pincherle, S. Acta Mth. 10 (1887) 153-. 



. Viterbi, A. Em. E. Ac. Line. 



Ed. 6 (1897) (Sen. 1) 247-. 



logarithms and Euler's constant. 

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

 (1891) No. 6, 15 pp. 



and series. Glaisher, J. W. L. Mess. 



Mth. 22 (1893) 97-. 

 summation of series. Graindorge, J. 



Liouv. J. Mth. 18 (1873) 129-. 

 sums deduced from Bernoulli function. 



Raabe, J. L. Crelle J. 42 (1851) 348-. 

 in theory of heat. Russell, W. H. L. 



Camb. and Dubl. Mth. J. 8 (1853) 157-. 

 . Meyer, G. F. Mth. A. 3 



(1871) 157-. 



uniformly convergent. Selivanoff, . 

 Par. S. Mth. Bll. 10 (1882) 147-. 



used for expanding functions in series. 

 Deflers, . Par. S. Phlm. Bll. (1819) 161-. 



integration. Rawson, R. [1844] Manch. 

 Ph. S. Mm. 7 (1846) 464-. 



as element of operation in mathematics. 



Viterbi, A. A. Mt. 26 (1897) 261- ; 3 (1899) 

 299-. 



, paradox. Walton, W. QJ. Mth. 6 

 (1864) 319-. 



, theorem. Glaisher, J.W.L. QJ. Mth. 



10 (1870) 347-. 

 , , general. Boole, G. Liouv. J. Mth. 



13 (1848) 111- ; Camb. and Dubl. Mth. J. 4 



(1849) 14-. 

 , theorems. Glaisher, J. W. L. [1878] 



Mess. Mth. 8 (1879) 63-. 

 Definition of definite integral. Fouche, M. 



N. A. Mth. 15 (1896) 207-. 

 . Burali-Forti, C. N. A. Mth. 15 



(1896) 495-. 

 as limiting value of a sum. 



Thomae, C. J. Z. Mth. Ps. 21 (1876) 224-. 

 Derivation of two definite integrals. Zehfuss, 



G. Schlomilch Z. 7 (1862) 445-. 

 Determinant of definite integrals. Tissot, A. 



Liouv. J. Mth. 17 (1852) 177-. 



Evaluation 3260 



Determinant of definite integrals. Enneper, A. 



Z. Mth. Ps. 11 (1866) 69-. 

 Determinantal and generating functions of 



Abel. Bassani, A. Nap. Ac. At. 7 (1895) 



No. 9, 19 pp. 

 Determination of limits to values. Winckler, 



A. Wien Ak. Sb. 90 (1885) (Ab. 2) 528-. 

 by series. Frullani, G. Mod. S. It. Mm. 



20 (1828) 663-. 

 Differentiation. Lindman, C. F. Stockh. Ofv. 



38 (1881) No. 6, 3-. 

 . Lerch, M. Prag Ceske Ak. Fr. Jos. Ez. 



(Tfida 2) 2 (1893) Art. 34, 15 pp. ; Fschr. 



Mth. (1893-94) 479. 

 . Hallgren, E. Goteb. Hndl. 32 (1897) 83-; 



Fschr. Mth. (1897) 255. 

 Dirichlet's integral. Kronecker, L. Berl. Ak. 



Sb. (1885) 641-. 

 Discontinuous integrals connected with series 



for (l-2px + x 2 )~l. Hamilton, (Sir) W. R. 



Ph. Mg. 20 (1842) 288-. 

 Division into elements, mode. Petrovitch, M. 



C. E. 122 (1896) 27-. 



Evaluation. 



Ellis, R. L. Camb. Mth. J. 3 (1843) 185- ; 



Liouv. J. Mth. 9 (1844) 422-. 

 Lobatschewsky, W. Erman Arch. Es. 14 (1855) 



232-. 

 Gegenbauer, L. Wien Ak. Sb. 64 (1871) (Ab. 2) 



703-. 



Todhunter, I. E. S. P. 23 (1875) 300-. 

 Hocevar, F. [1876] Wien Ak. Sb. 74 (1877) 



(Ab. 2) 155-. 



Appell, P. C. E. 87 (1878) 874-. 

 Spitzer, S. Arch. Mth. Ps. 62 (1878) 221-. 

 approximate. Dirksen, E. H. Berl. Ab. (1831) 



117-. 

 . Schlomilch, 0. Grunert Arch. 9 (1847) 



215-. 

 . Grunert, J. A. Grunert Arch. 14 (1850) 



225-. 

 . Araldi, A. [1859] (ix) Mod. Ac. Sc. 



Mm. 3 (1861) 65-, 137. 

 . Andr<e, G. G. G. Kjob. Ov. (1867) 165- ; 



Resume 26-. 



. Deruyts,J. Brux. Ac, Bll. 11 (1886) 307-. 

 . Berger, A. Ups. S. Sc. N. Acta 16 (1893) 



No. 4, 52 pp. 

 . Moors, B. P. N. Arch. Wisk. 20 (1893) 



129- ; 3 (1898) 285- ; Fschr. Mth. (1893-94) 



Bugaev, N. V. Kazan S. Ps.-Mth. Bll. 7 

 (1898) 95- ; Fschr. Mth. (1897) 258-. 



. Tschebyschew, P. L. Fschr. Mth. (1899) 

 279. 



formula. Radau, R. Liouv. J. Mth. 6 

 (1880) 283-. 



, and functions derived therefrom. Sonine, 



N. J. Fschr. Mth. (1887) 282-. 

 , Gauss's formula. Schellbach, C. H. Crelle 



J. 16 (1837) 192-. 

 , integral for compound survivorship annuity. 



Todhunter, R. I. Act. J. 33 (1898) 311-. 

 , method, Cotes-Gauss. Minich, S. R. Ven. 



At. 3 (1852) 7-. 



277 



