3220 Convergence 



rules. Bertrand,J. Liouv. J. Mth.7(1842)35-. 

 . Paucker, M. G. von [1849] Crelle J. 42 



(1852) 138-. 

 of series arising from development of functions, 



Cauchy's theorem, extension. Timmermans, 



J. A. Brux. Ac. Bll. 13 (1846) (pte. 2) 17-. 

 with complex terms. Benthem, A. N. 



Arch. Wisk. 2 (*1876) 186-. 

 and continued products. Eees, JR. van. 



Quetelet Cor. Mth. 6 (1830) 185-. 

 definite integrals. Chartier, J. Liouv. 



J. Mth. 18 (1853) 201-. 

 . Popper, J. Wien Sb. 52 (1866) 



(Ab. 2) 496-. 

 (Popper). Bugaev, N. V. (xn) 



Kec. Mth. (Moscou) 2 (1867) (Pt. 2) 81-. 

 . Ermakov, V. P. [1872] (xn) 



Bee. Mth. (Moscou) 6 (1872-73) (Pt. 1) 39-. 

 formed from prime powers of natural num- 

 bers. Martens, F. Gott. Nr. (1887) 265-. 



, general term of which is n x Laplace's 

 coefficient Y n . Plarr,G. C.K. 44 (1857) 835-. 



for p (u) and calculation of u. Soderblom, 



A. tips. S. Sc. N. Acta 14 (1891) No. 5, 67 pp. 



representing integrals of differential 

 equations. Picard, E. Bll. Sc. Mth. 12 

 (1888) 148-. 



. Staeckel, P. C. E. 126 



(1898) 203-. 

 system of differential equations. 



Cauchy, A. L. C. E. 10 (1840) 939-; 11 



(1840) 730- ; 40 (1855) 330-, 373-. 

 roots of equations, etc. Cauchy, A. L. 



C. E. 4 (1837) 216-. 

 for solution of Kepler's problem. Carlini, 



F. As. Nr. 30 (1850) 197-. 

 in theory of planetary motion. Puiseux, 



V. Liouv. J. Mth. 14 (1849) 33-, 243-. 

 . Serret, J. A. C. E. 42 



(1856) 1134-. 

 theorem. Malmsten, C. J. Grunert Arch. 6 



(1845) 38-. 

 . Delarue, D. M. (xn) Kharkov Mth. S. 



Com. (1879) 19-. 

 , general. Jensen, J. L. W. V. C. E. 106 



(1888) 729-. 

 , geometrical proof. Dixon, A. C. Camb. 



Ph. S. P. 8 (1895) 217-. 

 theorems. Scheibner, W. Leip. B. 25 (1873) 



568-. 

 , elementary. Oppermann, L. H. F. (xn) 



Ts. Mth. 3 (1873) 145-. 

 uniform. Cayley, A. Edinb. E. S. P. 19 



(1893) 203-. 



. Bendixson, I. Stockh. Ofv. (1897) 605-. 

 , application of notion. La Vallee-Poussin, 



C. J. de. Brux. S. Sc. A. 17 (1893) (Pt. 2) 



323-. 

 of variable series, degree. Du Bois-Reymond, P. 



Crelle J. Mth. 100 (1887) 331-. 



1 O K 



' ' + &e. Fontana, G. Verona S. It. 

 Mm. 3 (1786) 174-. 



2 -? . Lerch, M. Casopis 21 (1892) 



65-; Fschr. Mth. (1892) 232-. 



Infinite Series 3220 



Convergent and divergent series. Gamier, J. G, 

 Brux. Ac. Bll. 6 (1839) (Pte. 2) 113-, 262-. 



or divergent series, and continued fractions. 

 Fade, H. Acta Mth. 18 (1894) 97-. 



series. Cauchy, A. L. C. E. 36 (1853) 454-. 

 , continuity of values. Duhamel, J. M. C. 



C. E. 36 (1853) 643-. 



, Euler's condensation formula. Stud- 

 nicka, F. J. Casopis 1 (1872) 33- ; Bll. Sc. 

 Mth. As. 6 ("1874) 91. 



, limit. Friedlander, J. Gould. As. J. 3 



(1854) 129-. 

 Conversion into infinite products. Stern, M. A. 



Crelle J. 12 (1834) 353- ; N. A. Mth. 6 (1847) 



437-. 

 Deduction from infinite products. Glaisher, 



J. W. L. Mess. Mth. 2 (1873) 138-, 153-. 

 Derivation of negative powers (Eisenstein's 



theory). Sylvester, J. J. QJ. Mth. 1 (1857) 



199-. 

 ( ). Glaisher, J. W. L. [1875] 



QJ. Mth. 14 (1877) 79-. 

 ( ). Cayley, A. [1875] QJ. 



Mth. 14 (1877) 83-. 

 new infinite series from given series by 



change of sign. Mildner, E. [1882] Wien 



Ak. Sb. 86 (1883) (Ab. 2) 999-. 

 Derived series, theory. Werner, 0. Grunert 



Arch. 22 (1854) 264-. 

 Differentiation of products of terms of a series. 



Collins, E. [1826] St Pet. Ac. Sc. Mm. 1 



(1831) 3-. 

 series. Schlomilch, 0. Grunert Arch. 



10 (1847) 74-. 

 . Dienger, J. Grunert Arch. 11 (1848) 



38. 

 . Lerch, . G. Teix. J. Sc. 11 (1892) 



107-. 

 Diminishing series with alternating signs. 



Oltramare, G. Crelle J. 45 (1853) 345-. 

 Dirichlet's paradox. Unferdinger, F. [1868-69] 



Wien Sb. 57 (1868) (Ab. 2) 621- ; 60 (1870) 



(Ab. 2) 591-. 

 . Schlomilch, 0. Z. Mth. Ps. 15 (1870) 



134-. 



series. Lerch, . C. E. 128 (1899) 1310-. 



, multiplication and non-vanishing. 

 Mertens, F. Crelle J. Mth. 117 (1897) 169-. 



, theory. Pringsheim, A. Mth. A. 37 



(1890) 38-. 

 Discontinuity. Schlomilch, O. Schlomilch 



Z. 4 (1859) 161-. 



of values, tests. Duhamel, J. M. C. Liouv. 

 J. Mth. 19 (1854) 112-. 



Discontinuous series, case. Mansion, P. Mess. 



Mth. 7 (1878) 57-. 

 , Eiemann's. Smith, H. J. S. [1881] 



Mess. Mth. 11 (1882) 1-. 

 Distribution of signs in a series. Cesdro, E. 



Em. E. Ac. Line. Ed. 4 (1888) (Sem. 2) 133-. 

 Divergence of a series. Unferdinger, F. Wien 



Sb. 55 (1867) (Ab. 2) 95-. 

 Divergent series. De Morgan, A. [1844] 



Camb. Ph. S. T. 8 (1849) 182-. 



. Young, J. E. B. A. Ep. (1844) (Pt. 2) 1. 



. Catalan, E. C. N. A. Mth. 17 (1859) 



195-. 



241 



