2910 Bernoulli's Numbers 



and Euler's, related expressions. Fields, J. C. 

 Am. J. Mth. 13 (1891) 191-. 



, relations between. Sheppard, W. F. 

 QJ. Mth. 30 (1899) 18-. 



-, theory. Stern, M. A. Gott. Ab. 23 



(1878) (Mth.) 44 pp.; 26 (1880) (Mth.) 45 pp. 

 , . Haussner, E. Gott. Nr. (1893) 



777-. 

 expression by definite integral. Hamilton, 



(Sir) W. R. Ph. Mg. 23 (1843) 360-., 

 formulae of Seidel and Stern. Lucas, E. Par. 



S.Mth. Bll. 8 (1880) 169-. 

 fractional part. Cesdro, E. A. Mt. 14 (1886- 



87) 221-. 

 function related to them, as Tn to n ! Glaisher, 



J. W. L. B. A. Bp. 42 (1872) (Sect.) 17-. 

 and functions, generalisation. Berger, A. 



Stockh. Ak. Hndl. Bh. 13 (Afd. 1) (1888) 



No. 9, 43 pp.; Stockh. Ofv. (1888) 433-; 



Acta Mth. 14 (1890-91) 249-. 

 fundamental theorems relating to. Glaisher, 



J.W.L. Mess. Mth. 29 (1900) 49-, 129-. 

 general expression. Genocchi, A. Tortolini 



A. 3 (1852) 395-. 

 of higher orders. Grigorjev, E. Kazan S. 



Ps.-Mth. Bll. 7 (1898) 146- ; Fschr. Mth. 



(1898) 221-. 

 independent expression for. Berger, A. Stockh. 



Ofv. (1889) 129- ; Fschr. Mth. (1889) 247. 



representation. Ndgelsbach, H. Z. Mth. 

 Ps. 19 (1874) 219-. 



logarithms of first 40. Thoman, F. C. B. 50 



(1860) 905-. 

 method of finding. Canterzani, S. Mod. Mm. 



S. It. 11 (1804) 173-. 

 new expression for. Teixeira, J. P. Lisb. J. 



Sc. Mth. 3 (1895) 73-. 



recursion formula. Eogel, F. Prag Sb. 

 (1895) (Mth.-Nt.) No. 26, 4 pp. 



numbers a n< m in proof of Staudt's theorem. 

 Ely, G. S. (xn) J. H. Un. Cir. [2] (1883) 



analogous to. Matter, K. Ziir. Vjschr. 

 45 (1900) 238-. 



and Pascal's arithmetical triangle, relations of. 



Lucas, E. N. A. Mth. 15 (1876) 497-. 

 properties. Stern, M. A. Crelle J. Mth. 81 



(1876) 290- ; Bll. Sc. Mth. 10 (1886) 280-. 

 . Lipschitz, . D. Nf. B. (*1883) 56-. 

 property, proof. Glaisher, J. W. L. Mess. 



Mth. 2 (1873) 190-. 

 recurring determination. Schlomilch, O. Gru- 



nert Arch. 3 (1843) 9-. 



(Schlomilch). Gopel, A. Grunert 

 Arch. 3 (1843) 64-. 



formulas involving. Glaisher, J. W. L. 

 Mess. Mth. 28 (1899) 36-. 



and related functions. Le Paige, C.M.M.H.H. 



(xn) Brux. S. Sc. A. 1 (1877) (Pt. 2) 43-. 

 series, simple method of deducing. Seidel, 



P. L. von. Munch. Ak. Sb. 7 (1877) 157-. 



secant coefficients. Schlomilch, 0. Grunert 

 Arch. 1 (1841) 360-. 



. Meyer, G. F. Grunert Arch. 35 



(1860) 449-. 

 .formula for. Schlomilch, 0. Crelle J. 



32 (1846) 360-. 



Special Numbers, etc. 2910 



Bernoulli's Numbers, continued. 



and secant coefficients, general expression for 



both. Scherk,H.F. Crelle J. 4 (1829) 299-. 

 sum and difference formulae. Bauer, G. [1860] 



Crelle J. 58 (1861) 292-. 

 table of first 62. Adams, J. C. [1877] Crelle 



J. Mth. 85 (1878) 269-. 

 tables of 250, and their logarithms. Glaisher, 



J. W. L. [1871-72] Camb. Ph. S. T. 12 



J.873) 384-. 

 their composition from integers and re- 

 ciprocal primes. Zeller, C. Bll. Sc. Mth. 



As. 5 (1881) (Pt. 1) 195-. 

 theorem. Staudt, G. K. C. von. Crelle J. 



21 (1840) 372-. 



(Staudt). Schlafli,L. QJ. Mth. 6 (1863) 75-. 

 , Staudt-Clausen. Catalan, E. C. Bll. Sc. 



Mth. As. 4 (1880) 77-. 

 , . Lucas, E. Par. S. Mth. Bll. 11 



(1883) 69-. 

 , . Cesdro, E. Brux. Ac. Bll. 20 



(1890) 280-. 

 , . Kluyver, J. C. Mth. A. 53 (1900) 



591-. 

 , , and Binet's theorem. Lucas, E. 



N. A. Mth. 16 (1877) 157-. 

 ultra-Bernoullian numbers. Trudi, N. Nap. 



At. I. Inc. 4 (1867) 105-. 



Bernoulli's series. Sonin, N. St Pet. Ac. Sc. 



Bll. 7 (1897) 337-; Fschr. Mth. (1897) 224. 

 , condition for first n terms being a given 



function. Hill, C. J. D. Stockh. Ofv. 14 



(1857) 259-. 

 , constants occurring in summations by. 



Glaisher, J. W. L. [1872] L. Mth. S. P. 4 



(1871-73) 48-. 

 , series of differences of terms of. Markoff, 



A. Mth. A. 19 (1882) 27-. 

 Cauchy's numbers. Chessin, A. S. A. Mth. 



10 (1895-96) 1-. 

 , and their application to astronomy. 



Bourget, J. Liouv. J. Mth. 6 (1861) 33-. 

 , Bessel's functions, relation between. 



Chessin, A. S. A. Mth. 12 (1898-99) 170-. 

 Clapeyron's numbers, properties. olin, J. M. 



Prag Sb. (1878) 146-. 

 Constant which occurs in formula for 



I 1 . 2 s . 3 s ... n". Glaisher, J. W. L. Mess. 



Mth. 24 (1895) 1-. 

 Dirichlet's series. Hadamard, . Bordeaux 



S. Sc. PV. (1896-97) 41-. 

 Discontinuity factors, arithmetical. Eogel, F. 



Arch. Mth. Ps. 17 (1900) 147-. 

 Discontinuous function, Biemann's. Frischauf, 



J. Z. Mth. Ps. 34 (1889) 193-. 



functions. Sokolov, D. N. Bee. Mth. (Mos- 

 cou) 16 (1893) 282-; Fschr. Mth. (1892) 187. 



logarithmic functions. Bougalef, . C. B. 

 106 (1888) 1067-. 



Divisors of number. Hermite, C., & Lipschitz, 



R. Acta Mth. 2 (1883) 299-. 

 , formula of Hermite. Busche, E. 



Crelle J. Mth. 100 (1887) 459- ; 103 (1888) 125. 

 , theorems. Bougaief, N. C. B. 120 



(1895) 432-. 



229 



