2910 Special Numbers, etc. 



E(x), properties. Stern, M. A. [1860] Crelle 



J. 59 (1861) 146-. 



. Sylvester, J. J. C. E. 50 (1860) 732-. 

 , theorems. Bouniakowsky, V. C. E. 94 



(1882) 1459- ; St Pet. Ac. Sc. Bll. 28 (1883) 



257-, 411- ; 29 (1884) 250-, 503-. 

 . Hermite, . Am. J. Mth. 6 (1884) 173-. 

 , representation by an infinite series. Prings- 



heim, A. Mth. A. 26 (1886) 193-. 

 . Stern, M. A. Acta Mth. 8 (1886) 93-; 



10 (1887) 53-; Crelle J. Mth. 102 (1888) 9-; 



106 (1890) 337-. 

 . Mansion, . Brux. S. Sc. A. 13 



(Pt. 1) 55-. 

 . Giuliani, . Palermo Cir. Mt. Ed. 5 



(1891) 285-. 

 with complex argument. Busche, E. [1892- 



93] Crelle J. Mth. 110 (1892) 338- ; Hamb. 



Mth. Gs. Mt. 3 (1900) 103-. 

 , formulae concerning. Lerch, . G. Teix. 



J. Sc. 12 (1895) 129-. 

 . Bertolani, G. G. Mt. 34 (1896) 1-. 

 <b~ l (JT'), finding. Cayley, A. Ph. Mg. 14 



(1857) 539-. 

 F(x). Liauville, J. Liouv. J. Mth. 5 (1860) 



287-, 455-. 

 N(n, p, q). Liauville, J. Liouv. J. Mth. 6 



(1861) 369-. 

 E, numerical identities connected with. Bu- 



gaev, N. V. (xn) Eec. Mth. (Moscou) [1] 



(1866) i-, 1-. 

 , etc., equations depending on. Bugaev, 



N. V. [1874] (xn) Eec. Mth. (Moscou) 7 



(1874-75) (Pt. 1) 424-; (ix) Bll. Sc. Mth. 



As. 10 (1876) 102-. 

 E (ax + b) + 1 - (ax + b) . CebySev , P. [1866] 



St Pet. Ac. Sc. Mm. (Es.) 10 (*1867) 



(Suppl.) No. 4, 54 pp. 

 F(k), theorem. Liouville, J. Liouv. J. Mth. 



14 (1869) 1-, 260-. 

 j (n), expressing sum of divisors of n. Liouville, 



J. Liouv. J. Mth. 14 (1869) 263-. 



(n). Liouville, J. Liouv. J. Mth. 14 (1869)302-. 

 and $ (n, N). Smith, H. J. S. L. Mth. 

 P. 7 (1875-76) 208-. 

 (H. J. S. Smith). Mansion, P. (xn) 



Brux. S. Sc. A. 2 (1878) (Pt. 2) 211-. 

 \f/ (a) of Jacobi, theory. Schwering, K. Crelle 



J. Mth. 93 (1882) 334-. 



-}, theorem of Stieltjes. 



. 

 2 (n). 



(n) 

 S. 



Cesdro, E. G. E. 96 (1883) 1029-. 

 u, properties. Cesdro, E. N. A. Mth. 3 (1884) 

 431. 



E ( ^ J . Gram, J. P. Ts. Mth. 2 (1884) 170-. 



z - [z] . Cesdro, E. A. Mt. 13 (1885) 323-. 

 C (z). Cesdro, E. A. Mt. 13 (1885) 329-. 

 X (n) . Glaisher, J.W.L. QJ. Mth. 20 (1885) 97-. 

 X fc (n). Gegenbauer, L. Wien Ak. Sb. 96 



(1888) (Ab. 2) 607-. 

 $(p, q), theorems. Lerch, M. Bll. Sc. Mth. 



12 (1888) 121-. 



X=i ? 



x-i P] ' Busche ' E - CreUe J< Mth ' 106 

 X (1890) 65-. 



Transcendental Numbers 2920 



(x). Kronecker, L. Crelle J. Mth. 106 (1890) 



346-. 

 , applications. Hacks, J. Acta Mth. 14 



(1890-91) 329-. 

 N(n) and L(n). Gram, J. P. [1890] Kjrfb. 



Dn. Vd. Selsk. Skr. 7 (1890-94) 1-. (With 



French resume.) 

 a- (n), recurring formula for. Glaisher, J. W. L. 



Mess. Mth. 21 (1892) 122-. 



in theory of numbers (with tables). Mertens, 

 F. Wien Ak. Sb. 106 (1897) (Ab. 2a) 761-. 



, course of. Daublebsky von 



Sterneck, R. Wien Ak. Sb. 106 (1897) (Ab. 

 2a) 835-. 



E (n), Cesaro's formula. Oltramare, G. As. 

 Fr. C. E. (1893) (Pt. 2) 287-. 



p ()=nP (l - I) (l> 1) ... . Cistlakov, 



I. I. [1894] Eec. Mth. (Moscou) 17 (1895) 

 530- ; Fschr. Mth. (1893-94) 269-. 



Liouv. J. 



2km 

 h 



. 5 



Seguier, P. de. 

 55-. 



2920. Irrationality and transcend- 

 ence of particular numbers, 

 such as and T. (See also 

 6810.) 



Eisenstein's theorem on series for root of alge- 

 braic equation. Hermite, C. L. Mth. S. P. 

 7 (1875-76) 173-. 



. Gomes Teixeira, F. 



Arch. Mth. Ps. 3 (1886) 315-. 



Exponential function. Hermite, C. C. E. 77 

 (1873) 18-, 74-, 226-, 285-. 



, irrationality and transcendence. 

 Stieltjes, . C. E. 110 (1890) 267-. 



Irrational quantities, algebraic, theorem. Liou- 

 ville, J. C. E. 18 (1844) 910-. 



Transcendental numbers deduced from proba- 

 bilities. Bouniakowski, F. St Pet. Ac. Sc. 

 Bll. 1 (1836) 177 ; St Pe"t. Ac. Sc. Mm. 3 

 (1838) 457-, 517-. 



, two theorems. Gronwall, H. Stockh. 



Ofv. (1897) 623-; (1898) 153-. 



e. 



Leclerc, . N. A. Mth. 14 (1855) 225-. 

 Paque, A. Liege Mm. S. Sc. 10 (1855) 199-. 

 Eealis, S. N. A. Mth. 6 (1867) 541- ; 7 (1868) 



16-, 158-, 191-. 

 arithmetical character. Borel, E. C. E. 128 



(1899) 596-. 

 calculation. Bretschneider, C. A. Grunert 



Arch. 3 (1843) 27-. 

 . Studnicka, F. J. Casopis 20 (1891) 61- ; 



Fschr. Mth. (1891) 440-. 



from continued fraction. Glaisher, J. W. L. 

 B. A. Ep. 41 (1871) (Sect.) 16-. 



and continued fraction, relation between. 



Cailler, . As. Fr. C. E. (1889) (Pt. 2) 158-. 

 irrationality. Gruson, J. P. Berl. Ab. (1816- 



17) 18-. 

 . Liouville, J. Liouv. J. Mth. 5 (1840) 192-. 



232 



