Infinite Series 



3220 



Power Series, continued. 



of two variables, regions of convergence. 



Zindler, K. Mh. Mth. Ps. 4 (1893) 115-. 

 unique development of function. Mourner, 



G. J. D. N. Arch. Wisk. 19 (1892) 100- ; 



Fschr. Mth. (1892) 360. 



Problem. Petrovitch, M. N. A. Mth. 15 



(1896) 58-. 

 Product of two series of form 



1 + a - +a(a + k) j-^ +&c. 



is of same form. Stainville, de. Ger- 



gonne A. Mth. 9 (1818-19) 229-. 

 Products and sums, determination of real 



numbers by. Giudice, F. Tor. Ac. Sc. At. 



29 (1894) 188-. 

 Progression, geometrical, theorem. Meech, 



L. W. Gould As. J. 4 (1856) 65-. 

 Progressions. Toledo, L. 0. de. Fschr. Mth. 



(1899) 244. 

 , geometrical. Heis, E. Grunert Arch. 6 



(1845) 104-. 

 , , of higher order. Eetali, V. G. Mt. 11 



(1873) 349-. 



, , solution of problem supposed inde- 

 terminate. Rotheram, J. Manch. Ph. S. 

 Mm. 3 (1790) 330-. 



, , theorems. Blackburne, C. Ph. Mg. 6 

 (1835) 196- ; B. A. Ep. (1837) (ft. 2) 2. 



of higher order. Bonolis, A. G. Mt. 12 



(1874) 179-, 231-. 



various orders. Cauchy, A. L. C. E. 



20 (1845) 2-. 

 . Le Cointe, J. L. A. [1863] A. 



Mt. 6 (1864) 124-. 

 Properties. Nielsen, N. N. Ts. Mth. 3 (B) 



(1892) 91- ; Fschr. Mth. (1892) 231-. 



of a class of series. Lipschitz, R. Crelle 

 J. Mth. 105 (1889) 127- ; 106 (1890) 27-. 



Property. Schlomilch, 0. Schlomilch Z. 3 



(1858) 130-. 



. Kdnigsberger, L. Mth. A. 27 (1886) 397-. 

 Eational relations between certain series. 



Nielsen, N. N. Ts. Mth. 8 (B) (1897) 7-; 



Fschr. Mth. (1897) 228-. 

 Eecurring relations in coefficients of series, 



especially Bernoulli's numbers. Berg, F. J. 



van den. [1880?] Amst. Ak. Vs. M. 16 (1881) 



74-; Arch. Neerl. 16 (1881) 387-. 

 Eeduced forms (reduites) of exponential function , 



convergence. Pade,H. C. E. 127 (1898) 444-. 

 Eeduction, general method. Baton de la 



Goupilliere, J. N. C. E. 44 (1857) 1145- ; 



Par. FJC. Pol. J. 37 cah. (1858) 97-. 

 Eemarkable class. Bjorling, E. G. Stockh. 



Ak. Hndl. (1846) 17-; Liouv. J. Mth. 17 



(1852) 454-. 



series. Hessel, J. F. C. Grunert Arch. 5 

 (1844) 287-. 



Eepresentation by integrals. Kronecker, L. 



Crelle J. Mth. 105 (1889) 157-, 345-. 

 Eesidue, Jacobi's method for determination. 



Scheibner, W. Leip. Mth. Ps. B. 45 (1893) 432-. 

 Eeversion. Canterzani, S. Verona Mm. S It 



5 (1790) 88-. 



Eeversion. Brinkley, J. [1798] Ir. Ac. T. 7 



(1800) 321-. 



. Degen, C. F. As. Nr. 2 (1824) 243-. 

 . Collins, E. [1831] St Pet. Ac. Sc. Mm. 



2 (1833) 31-. 



. Mobius, A. F. Crelle J. 9 (1832) 105-. 

 . Sylvester, J. J. E. S. P. 7 (1854-55) 



219-. 

 . Mainardi, G. Mil. At. I. Lomb. 1 (1858) 



90-. 



(Mainardi). Bellavitis, G. Ven. At. (1857- 

 58) 623- ; (1858-59) 334-. 



. Glaisher, J. W. L. Mess. Mth. 6 (1877) 



142- ; Ph. Mg. 18 (1884) 518-. 

 . McMahon, J. N. Y. Mth. S. Bll. 3 (1894) 



170-. 

 , formula. Cayley, A. [1855-57] Crelle J. 



52(1856)276-; 54(1857)156-. 

 , general coefficient. Martynowski, J. Brux. 



Ac. Bll. 4 (1837) 135. 

 Secant series, coefficients. Stern, M. A. 



Crelle J. 26 (1843) 88-. 

 Semi-convergent series. Glaisher, J. W. L. 



[1872] QJ. Mth. 12 (1873) 52-. 

 . Stieltjes, T. Par. EC. Norm. A. 3 



(1886) 201-. 

 , arbitrary constants as multipliers. 



Stokes, (Sir) G. G. Camb. Ph. S. P. 6 (1889) 



362-. 

 , multiplication. Cajori, F. Am. J. 



Mth. 15 (1893) 339-; N. Y. Am. Mth. S. 



Bll. 1 (1895) 180-. 

 , and involution. Cajori, F. Am. 



J. Mth. 18 (1896) 195-. 

 , order of terms. Manning, H. B. 



Am. J. Mth. 16 (1894) 151-. 

 , , change. Borel, E. Bll. 



Sc. Mth. 14 (1890) 97-. 



, use of Bernoulli's function in ex- 

 pansion. Schlomilch, O. Schlomilch Z. 1 



(1856) 193-. 

 Series for any binomial power. Euler, L. 



[1779] St Pet. Ac. Sc. Mm. 4 (1813) 



75. 

 , coefficients of which are in arithmetical 



progression. Grunert, J. A. Grunert Arch. 



9 (1847) 322-. 

 , inverses of binomial coefficients. 



Roberts, S. Mess. Mth. 9 (1880) 166-. 

 , involve powers of Bernoullian 



numbers. Glaisher, J. W. L. Mess. Mth. 



19 (1890) 138-. ' 

 , proceed by sines and cosines of 



multiple angles. Tralles, J. G. Berl. Ab. 



(1820-21) 137-. 



of continuous functions, continuity of sum. 

 Arzela, C. Bologna Ed. (* 1883-84) 79-. 



cubes. Simon, 0. E. Grunert Arch. 27 



(1856) 313-. 



and definite integrals. Kummer, E. E. 

 Crelle J. 17 (1837) 210-, 228-. 



(Kummer). Giuliani, G. G. Mt. 



26 (1888) 234-. 

 . Glaisher, J. W. L. Mess. Mth. 



22 (1893) 97-. 

 , theory. Pringsheim, A. Mth. A. 



37 (1890) 591-. 



246 



