3260 



Integration of / ^ dx by integration of 



J o I + * 



differential equations. Veltmann,W. Grunert 



Arch. 38 (1862) 337-. 

 Inverse calculus. Boole, G. Camb. Mth. J. 4 



(1845) 82-. 



. Bronwin, B. Ph. Mg 31 (1847) 12-. 



. Rouche, E. C. B. 51 (1860) 126-. 



. Laurent, H. Liouv. J. Mth. 4 (1878) 225-. 



method. Murphy, R. [1832-35] Camb. Ph. 

 S. T. 4 (1833) 353- ; 5 (1835) 113-, 315-. 



Inversion. Pincherle, S. Mil. I. Lomb. Ed. 



20 (1887) 376-. 

 . Levi-Civita, T. Tor. Ac. Sc. At. 31 (1895) 



25-. 

 . Volterra, V. Tor. Ac. Sc. At. 31 (1895) 



231-, 286-, 389-, 429- or 311-, 400-, 557-, 



693-; Em. E. Ac. Line. Ed. 5 (1896) (Sem. 1) 



177- ; A. Mt. 25 (1897) 139-. 

 . Holmgren, E. [1899-1900] Stockh. Ak. 



Hndl. Bh. 25 (1900) (Afd. 1) No. 3, 19 pp.; 



Ups. S. Sc. N. Acta 20 '(1904) No. 2, 32 pp. 



(Volterra's theorem). Holmgren, E. Tor. 

 Ac. Sc. At. 35 (1900) 384- or 570-. 



Law of reciprocity in, cases. Cauchy, A. L. 



Par. S. Phlm. Bll. (1817) 121-. 

 Legendre's formula, generalisation. Lerch, M. 



[1891] Prag Ceske Ak. Fr. Jos. Ez. (THda 2) 



1 (1892) Art. 8, 37-. 

 Limit given by an inequality. Gomes Teixeira, 



F. Bll. Sc. Mth. 12 (1888) 288-. 

 Limiting ratio of two integrals. Cesdro, E. 



Bll. Sc. Mth. 17 (1893) 321-. 

 Limits, two. Hermite, C. (xn) Mathesis 3 



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to oo . Malmsten, C. J. Ups. N. Acta S. 

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Line and surface integrals, new demonstration 

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Maxima and minima. Zimmerman, V. A. Eec. 

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 , convergence. Cavallin, B. B. S. 

 Stockh. Ak. Hndl. Bh. 15 (Afd. 1) 

 No. 3, 17 pp. 

 .criteria. Zmurko, L. [1875-76] D. Nf . 



Definite Integrals (simple) 



3260 



Peano's concept. Stolz, 0. Mh. Mth. Ps. 7 



(1896) 291- ; 8 (1897) 95-. 

 Poisson's integral, applications. La Vallee- 



Poussin, C. J. de. Brux. S. Sc. A. 17 (1893) 



(Pt. 2) 18-. 

 and its conjugate. Tauber,A. Mh. Mth. 



Ps. 6 (1895) 109-, 302. 

 Proof of equality. Heine, H. E. Crelle J. 50 



(1855) 323-. 

 Properties. Winckler, A. Wien SB. 43 (1861) 



(Ab. 2) 315-. 



deduced from elliptic coordinates. Roberts, 

 W. Liouv. J. Mth. 16 (1851) 1-. 



, general. Murphy, R. Camb. Ph. S. T. 3 



(1830) 429-. 

 Seduction. Roberts, (Rev.) W. R. [1900] Ir. 



Ac. P. 6 (1900-02) 93-. 

 , formula. Schlomilch, O. Grunert Arch. 



9 (1847) 379-. 

 , formulae. Bierens de Haan, D. Arch. Neerl. 



5 (1870) 447-; Amst. Vh. Ak. 12 (1871) 65 pp. 

 , method and applications. Haan, D. 



Bierens de. Amst. Vh. 2 (1855) 54 pp. 

 Eesolution into other definite integrals with 



narrower limits. Schlomilch, 0. Grunert 



Arch. 4 (1844) 316-. 

 Simultaneous representation. Kowalewski, G. 



Crelle J. Mth. 117 (1897) 267-. 

 Singular definite integrals. Cauchy, A. L. 



C. E. 16 (1843) 422-. 



values. Schlomilch, 0. Grunert Arch. 11 

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Solution of equations by definite integrals. 

 Du Bois-Reymond, P. [1871] Crelle J. 74 

 (1872) 281-. 



problems by definite integrals. A bel, N. H. 



Mg. Ntvd. 2 (1823) 55-, 205-. 



Substitution of non-periodic for periodic func- 

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Summation of Gaussian series by definite in- 

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 (1889) 267-. 



series by definite integrals. Lejeune- 

 Dirichlet, G. Berl. Ab. (1835) 391- ; Crelle 

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. Dienger, J. [1847] Crelle 



J. 46 (1853) 119-. 



Tbl. (*1875) 177- ; Wien Ak. D. 37 (1877) . Smaasen, W. [1848] Crelle 



(Ab. 2) 43-. J. 42 (1852) 222-. 

 , . Mertens, F. Z. Mth. Ps. 21 . Dienger, J. Crelle J. 38 



(1876) 142-. 



, relative. Zmurko, L. Wien Ak. D. 



36 (1876) (Ab. 2) 235-. 



(1849) 266-, 331- ; 41 (1851) 137-. 

 . Du Bois-Reymond, P. 



[1871] Crelle J. 74 (1872) 281-. 



, values. Liventsov, A. I. [1879] (xn) . Petrovitch, . C. E. 120 



Eec. Mth. (Moscou) 10 (1882-83) (Pt. 1) 70-. (1895) 819-. 

 , , determination. Markov, A. A. . Rogel, F. Prag Sb. (1895) 



(xn) Kharkov Mth. S. Com. (1883) 95-; 



Fschr. Mth. (1885) 168, 171. 

 Mean values. Hauber, C. F. Baumgartner Z. 



8 (1830) 25-, 147-, 295-, 443-; 9 (1831) 302- ; 



10 (1832) 425-. 

 . Pleskot, A. Prag Ceske Ak. Fr. Jos. 



Ez. (Tfida 2) 2 (1893) Art. 6, 6 pp. ; Fschr. 



Mth. (1893-94) 475-. 

 Methods. Tait, P. G. [1879] Edinb. E. S. P. 



10 (1880) 271. 

 Multiplication. Russell, W. H. L. [1874] E. S. 



P. 23 (1875) 120-. 



(Mth.-Nt.) No. 39, 33 pp. 

 Synectic functions. Dillner, G. Ts. Mt. Fys. 



3 (1870) 257- ; 4 (1871) 33-, 121-. 

 Tables. Haan, D. Bierens de. Amst. Vh. 5 



(1858) 572 pp. 



(Bierens de Haan). Bellavitis, G. Ven. 

 At. (1858-59) 423-. 



( ). Lindman, C. F. Stockh. Ofv. 



33 (1876) No. 9, 7-; 35 (1878) No. 1, 3-; 

 Stockh. Ak. Hndl. Bh. 10 (1885) No. 3, 

 268 pp. ; Stockh. Ak. Handl. 24 (1890-92) 

 No. 5, 231 pp. 



279 



