2920 Transcendental Numbers 



irrationality. Thue, A. [1888] Arch. Mth. 

 Ntvd. 14 (1890) 251- ; Fschr. Mth. (1888) 263. 



and transcendence. Jamet, V. N. A. Mth. 



10 (1891) 215-. 



limits for. Ligowski, W. Arch. Mth. Ps. 57 



(1875) 220-. 

 new series for. Eados, G. Mth. Termt. Ets. 



11 (1893) 358-. 



transcendence. Cailler, C. As. Fr. C. R. 

 (1891) (Pt. 2) 83-. 



. Hurwitz,A. Gott. Nr. (1893) 153- ; C. B. 

 116 (1893) 788-. 



. Gordan, . C. E. 116 (1893) 1040-. 



, change in Hermite's first proof. Venske, 

 0. Gott. Nr. (1890) 335-. 



value to 205 places. Shanks, W. B. S. P. 6 

 (1854) 397- ; 20 (1872) 27-. 



/ l\ w 

 e=lim. (1 + -) . Liouville,J. Liouv. J. Mth. 



V n J 

 5 (1840) 280. 



= , expansion when n = oo . Spitzer, S. 

 Grunert Arch. 23 (1854) 127-. 



= , n an integer. Dcmkin, W. F. [1862] 

 QJ. Mth. 6 (1863) 1-. 



= , demonstration. Fort, 0. Schlomilch 

 Z. 7 (1862) 46-. 



i 



e = lim. (! + #)*, value when x = 0. Schulten, 

 N. G. of (fil.) [1842] Helsingf . Acta 2 (1847) 

 81. 



= , expansion. Wittstein, T. Grunert 

 Arch. 3 (1843) 327-. 



= ,. Frost, P. QJ. Mth. 7 (1866) 381-. 



e=lim. (1 + ax)*, expansion. Appell, P. Arch. 



=lim. (1 + ax)*, expansio 

 Mth. Ps. 65 (1880) 171-. 



e*, irrationality. Hermite, C. B. A. Bp. 43 

 (1873) (Sect.) 22-. 



e and IT, approximate numerical theorem. 



Glaisher, J. W. L. [1877] QJ. Mth. 15 



(1878) 125-. 

 , irrationality. Pads, H. Bll. Sc. 



Mth. 12 (1888) 144-. 

 , transcendence. Gordan, P. Mth. A. 



43 (1893) 222-. 



, . Hilbert, D. Gott. Nr. (1893) 113-. 



, . Mertens, F. Wien Ak. Sb. 105 



(1896) (Ab. 2a) 839-. 

 , . Jamet, V. Ens. Mth. 2 (1900) 



355-. 



Lindemann, C. L. F. Berl. Ak. Sb. (1882) 679- ; 



Mth. A. 20 (1882) 213-. 

 (Lindemann). Weierstrass, K. Berl. Ak. Sb. 



(1885) 1067-. 

 approximation. Belli, G. Brugnatelli G. 3 



(1820) 409-. 



. Catalan, E. C. N. A. Mth. 1 (1842) 190-. 

 . Caminati,P. As.Fr.C.B. (1887) (Pt.l) 173. 

 approximations. Barrois, T. Gergonne A. Mth. 



4 (1813-14) 360-. 



calculation. Fanien,A. N. A.Mth.9(1850) 190-. 

 . Dupain, J. C. N. A. Mth. 15 (1856) 82-. 

 . Frisby, E. [1872] Mess. Mth. 2 (1873) 114-. 

 . Glaisher, J. W. L. [1872] Mess. Mth. 2 



(1873) 119-. 



Analysis. General 3190 



calculation, elementary. Farcy, A. N. A. 



Mth. 3 (1844) 582-. 

 construction. Efimov, M. Kazan S. Ps.-Mth. 



Bll. 5 (1896) (Prot.) 66. 

 convergency of Euler's developments. Gra- 



bowski, E. Prace Mt.-Fiz. 3 (1892) 130- ; 



Fschr. Mth. (1892) 232. 

 error by method of isoperimeters. Hermann, A . 



N. A. Mth. 5 (1866) 509-. 

 formula for. Grebe, E. W. Grunert Arch. 12 



(1849) 181-. 

 geometric construction impossible. Saalschiitz, 



. Konigsb. Schr. 35 (1895) [23]-. 

 hyperbolic analogue. Studnicka, F. J. Liege 

 . S. Sc. Mm. 14 (1888) No. 6, 12 pp. ; Prag Sb. 



(1892) (Mth.-Nt.) 250-. 



, Laisant's, calculation. Studnicka, 

 F. J. Liege S. Sc. Mm. 17 (1892) No. 6, 7 pp. 



logarithm of. Glaisher, J. W. L. L. Mth. 

 S. P. 14 (1882-83) 134-. 



and its integral powers are incommensurable. 



Collignon, E. Par. S. Phlm. Bll. 3 (1879) 195-. 

 irrationality. Valat, . Bordeaux Act. Ac. 



Sc. 26 (1864) 269-. 

 , Lambert's proof, and irrationality of other 



quantities. Glaisher, J. W. L. B. A. Bp. 



41 (1871) (Sect.) 12-. 



and transcendence, proof. Sylvester, . 

 C. E. Ill (1890) 866-. 



. (Sylvester). Markow,A.A. Fschr. 



Mth. (1899) 386. 

 and powers of TT, series and products for. 



Glaisher, J. W. L. [1877] Mess. Mth. 7 



(1878) 75-. 

 series for. Glaisher, J. W. L. [1872] QJ. Mth. 



12 (1873) 232-. 



of Schwab for. Virieu, J. de. N. A. Mth. 

 18 (1859) 234-. 



. Tannery, J. Bll. Sc. Mth. As. 5 



(1881) 454-. 

 transcendence. Tognoli, 0. G. Mt. 24 (1886) 



354-. 

 . Brunei, . Bordeaux S. Sc. Mm. 2 (1891) 



xi-. 

 transformation of Leibnitz's series for. Polster, 



F. Arch. Mth. Ps. 63 (1879) 447-. 



- , Nicholson's formula for, discussion. Strnad, 



A. fiasopis 19 (1890) 144- ; Fschr. Mth. (1890) 

 261-. 



M (Briggs' modulus), value to 205 places. 

 Shanks, W. E. S. P. 6 (1854) 397-; 20 

 (1872) 27-. 



(For applications of arithmetical methods 

 to algebraic functions see 4010.) 



ANALYSIS 

 3190 General. 



La Place, P. S. (le marquis) de. Par. EC. Pol. 



J. 8 (1809) (15 cah.) 229-. 

 Herschel, (Sir) J. F. W. Phil. Trans. (1814) 



440-. 



233 



