3220 Summation 



Infinite Series 



Summation 3220 



of class of series. Frenet, F. [1856] Lyon 



Ac. So. Mm. 7 (1857) 59-. 

 . Andre, D. G. E. 88 (1879) 740-. 



compound series and application to proba- 

 bilities. Terrot, C. H. Edinb. E. S. T. 20 

 (1853) 541-. 



by continued fractions. Homer, W. G. Thom- 

 son A. Ph. 11 (1826) 416- ; 12 (1826) 48-. 



of convergent series, cases. Verniory, . 

 Mathesis 12 (1892) 265-. 



by development of (1 - ax cx z \~ m . Dienger, 

 J. [1847] Crelle J. 43 (1852) 88-. 



differential formulae. Euler, L. [1780] St 

 Pet. Ac. Sc. Mm. 5 (1815) 45-. 



of divergent series. De Morgan, A. Assur. 



Mg. 12 (*1866) 245-. 



. Borel, E. C. E. 121 (1895) 1125-. 



elementary. Bode, J. Grunert Arch. 34 



(1860) 397-. 

 of elementary series, cases. Nielsen, N. N. Ts. 



Mth. 7 (B) (1896) 63-; Fschr. Mth. (1896) 



208. 

 equation of coefficients occurring in summation. 



Eytelwein, J. A. Berl. Ab. (1820-21) 1-. 

 and expansion. Dienger, J. Grunert Arch. 7 



(1846) 430- ; 8 (1846) 450-. 

 formula. Frenet, F. C. E. 44 (1857) 1274-. 

 . Perrin, E. [1876] Par. S. Mth. Bll. 5 



(1877) 47-. 



. Laisant, C. A. As. Fr. C. E. (1878) 179-. 

 , Dorna's. Curtze, M. Arch. Mth. Ps. 46 



(1866) 357- ; 47 (1867) 238-. 

 , Euler's. Franel, J. Mth. A. 47 (1896) 



433-. 

 , or Maclaurin's. Malmsten, C. J. Acta 



Mth. 5 (1884) 1-. 



involving Bernoulli's numbers. Spitzer, S. 

 Grunert Arch. 23 (1854) 457-. 



for 3rd power of terms. Hellerung, . 

 Grunert Arch. 2 (1842) 198-. 



J reciprocal power series. Meyer, G. F. 



Arch. Mth, Ps. 41 (1864) 220-. 

 , universal. Meech, L. W. Gould As. J. 



2 (1852) 121-. 

 formulas. Young, J. E. Ph. Mg. 10 (1837) 



121- ; 11 (1837) 41-. 



. Genocchi,A. Tortolini A. 6 (1855) 70-. 

 , and Bernoulli's numbers. Bauer, G. [1860] 



Crelle J. 58 (1861) 292-. 



of Euler and Stirling, complementary terms. 

 Sonin, N. C. E. 108 (1889) 725-. 



, new. Lucas, E. N. A. Mth. 14 (1875) 487-. 

 of four algebraic series. Glaisher, J. W. L. 

 [1877] Mess. Mth. 7 (1878) 119-. 



geometric series, 2nd and higher orders, by 

 definite integrals. Glaisher, J. W. L. QJ. 

 Mth. 11 (1871) 328-. 



harmonic series. Malfatti, G. F. Turin 

 Mm. Ac. 4 (1788-89) 53-. 



investigations. Lorgna, A. M. Verona S. It. 



Mm. 1 (1782) 268-. 

 Kummer' s method, auxiliary functions. Bresse, 



. C. E. 64 (1867) 1023-, 1138-. 

 memoir by Goldbach, 1718. Enestrom, G. Bb. 



Mth. (1887) 23-. 

 method. Schlomilch, 0. Grunert Arch. 11 



(1849) 130-. 



, -. 



oon, E. Ph. Mg. 28 (1846) 136-. 

 s. Babbage, C. Phil. Trans. (1819) 



of negative powers of natural numbers. 

 Schlomilch, 0. X. Leip. Mth. Ps. B. 29 



(1877) 106-. 



neutral series. Young, J. E. Ph. Mg. 27 

 (1845) 362-, 437-. 



--- . Moon, E. 

 new methods. 



249-. 

 peculiarity. Schlomilch, 0. Grunert Arch. 10 



(1847) 45-. 

 of power series. Steen, A. (xn) Ts. Mth. 2 



(1878) 183- . 



powers of reciprocals of numbers. Warming, 

 E. Kjtfb. Dn. Vd. Selsk. Skr. 8 (1895-98) 395-. 



series of arcs. Dobinski, G. [1878] Arch. 

 Mth. Ps. 63 (1879) 393-. 



--- circular arcs. Grunert, J. A. Arch. 



Mth. Ps. 47 (1867) 361-. 

 -- with simple generating functions. Oet- 



tinger, L. Crelle J. 14 (1835) 262-, 330- ; 



15 (1836) 264-, 317-. 



of sines or cosines of multiple arcs. 

 Clausen, T. Crelle J. 4 (1829) 281-. 



whose law is known. Gruson, J. P. 

 Berl. Mm. Ac. (1804) 83-. 



slowly converging and diverging series. 

 Young, J. E. Ph. Mg. 6 (1835) 348-; 7 

 (1835) 25-. 



--- series. Kummer, E. E. Crelle J. 16 



(1837) 206-. 

 ---- . Lubbock, J. W. As. S. M. Not. 



10 (1849-50) 180-. 



---- . Fabian, 0. (xn) Krk. Ak. (Mt.- 



Prz.) Pam. 2 (1876) 37-. 

 ---- (alternate harmonic series), rapid. 



Janet, A. C. E. 118 (1894) 239-. 

 solution of two problems. Trowbridge, D. Des 



Moines Anal. 3 (1876) 154-. 

 of terms very far on. Cauchy, A. L. C. E. 



32 (1851) 389-. 



trigonometric and other series. Eogel, F. 

 Arch. Mth. Ps. 12 (1894) 37-. 



-- series. Adams, Jas. Thomson A. Ph. 



15 (1820) 335- ; 4 (1822) 21-. 

 --- . Macully, J. F. Mth. Misc. 2 (1839) 



118-. 

 --- . Dirksen, E. H. Berl. B. (1842) 



20-; (1843) 83-. 

 --- . Miiller, J. H. T. Grunert Arch. 



11 (1848) 439-. 



--- . Blissard, J. Mess. Mth. 2 (1863) 



50-. 

 --- , cases. Schulten, N. G. of (fil.) 



Stockh. Ak. Hndl. 40 (1819) 184-. 

 --- , . Talbot, W. H. F. Gergonne A. 



Mth. 14 (1823) 88-, 187-. 

 --- , . Catalan, E. C. N. A. Mth. 3 



(1844) 570-. 

 --- , . Dienger, J. Crelle J. 41 (1851) 



48-. 

 --- , . Eeinemund, F. Brux. Ac. Bll. 



40 (1875) 801- ; 43 (1877) 356-. 



,. Stprmer, C. Christiania F. 

 (1892) No. 17, 21 pp. 



--- , . Nielsen, N. Kjjzfo. Ov. (1896) 



348-. 

 --- , class. Glaisher, J. W. L. B. A. Ep. 



(1879) 269-. 



249 



