2910 



Special Numbers and Numerical Functions 



2910 



Divisors of number, theorems (Bougaief). 



Gegenbauer, L. Mb. Mth. Ps. 7 (1896) 26. 

 numbers, theorem of Bugaief. Gegen- 



bauer, L. Wien Ak. Sb. 95 (1887) (Ab. 2) 



219-. 

 Enumerative functions. Cesdro, E. A. Mt. 14 



(1886-87) 141-. 

 Equation 



residues and coefficients, analogy. Roselli, E. 

 Em. Cor. Sc. 1 (1848) 373-. 



*2 W _ Mangoldt, H. von. Berl. 



Ak7sb. (1897) 835-. 



Eulerian and other coefficients, congruence 

 theorem relating to. Glaisher, J. W. L. 

 L. Mth. S. P. 31 (1900) 193-. 



(/.-function. Busche, E. Mth. A. 31 (1888) 

 70-. 



--- . Baker, H. F. [1889] L. Mth. S. 



P. 21 (1891) 30-. 



Euler's constant, calculation. Glaisher, 

 . J. W. L. E. S. P. 19 (1871) 514-. 

 -- , expression for. Franklin, F. (xn) J. H. 



Un. Cir. [2] (1883) 143. 

 -- , history. Glaisher, J. W. L. [1871] 



Mess. Mth. 1 (1872) 25- ; 2 (1873) 64. 

 -- , logs e 2, 3, 5, 7, 10, to 260 places. 



Adams, J. C. E. S. P. 27 (1878) 88-. 

 -- , relation connecting constants analogous 



to. Glaisher, J. W. L. Mess. Mth. 24 



(1895) 24-. 



- -- , series for. Nielsen, N. N. Ts. Mth. 8 



(B) (1897) 10- ; Fschr. Mth. (1897) 235. 



, value to 260 places. Adams, J. C. B. 

 A. Ep. (1877) (Sect.) 14-. 



functions. Rogel, F. Prag Sb. (1893) 

 (Mth.-Nt.) No. 23, 52 pp. ; (1896) (Mth.-Nt.) 

 No. 2, 45 pp. 



numbers. Catalan, E. C. C. E. 66 (1868) 

 415-. 



- -- . Stern,M.A. CrelleJ.Mth. 79 (1875) 67-. 



- -- . Lucas, E. [1877] Mess. Mth. 7 (1878) 



139-. 



-- . Eadicke,A. CrelleJ.Mth. 89 (1880) 257-. 

 -- , an analogue of. Studnicka, F. J. Prag 



Sb. (1900) (Mth.-Nt.) No. 9, 8 pp. 



^, coefficients analogous to. Glaisher, 

 J. W. L. L. Mth. S. P. 31 (1900) 216-. 



Expansion of numerical functions in series. 



Lerch, . C. E. 108 (1889) 171-. 

 ------ . Rogel, F. Prag Sb. (1897) 



(Mth.-Nt.) No. 46 [44], 26 pp.; (1900) 



(Mth.-Nt.) No. 30, 7 pp. 



-- ce x -l ' Fer 9 la ' E ' Na P- Ac - Sc - Mm - 



2 (1855-57) 315-. 



- -- (f~ ^)" serie s- Lucas, E. [1877] 



Mess. Mth. 7 (1878) 82-. 

 -- ^ I in powers of x, series resulting 



from. Oltramare,G. As. Fr.C.E. (1881)117-. 

 Expansions , numerical . Cayley , A. Q J . Mth . 



3 (1860) 366-. 



Factorials, numerical, of 2nd order. Collins, E. 



[1835] St Pet. Ac. Sc. Mm. 3 (1838) 225-. 

 Formula of Gauss, generalisation. Busche, E. 



C. E. 129 (1899) 952-. 

 Function connected with divisors of a number. 



Glaisher, J. W. L. [1890] L. Mth. S. P. 



21 (1891) 395-. 



expressing 1 n - ' 



Minln, 



A. P. [1874] (xn) Eec. Mth. (Moscou) 7 

 (1874-75) (Pt. 1) 485-. 



relating to (4?n + l) and (4m + 3) divisors of 

 number. Glaisher, J. W. L. L. Mth. S. P. 

 15 (*1883-84) 104- . 



Functions, numerical. Liouville, J. Liouv. 



J. Mth. 2 (1857) 141-, 244-, 377-, 408, 409-, 



425-. 



, . Bellavitis,G. Ven. At. (1858-59) 536-. 

 , . Bouniakowsky, V. [1861] St Pet. 



Ac. Sc. Mm. 4 (1862) No. 2, 35 pp. 

 >-, . Liouville, J. Liouv. J. Mth. 8 (1863) 



347-. 

 , . Bugaev, N. V. [1867] (xn) Eec. Mth. 



(Moscou) 3 (1868) (Pt. 1) 69-. 

 , . Gegenbauer, L. Wien Ak. Sb. 89 



(1884) (Ab. 2) 37-. 



, , class. Cesdro, E. G. Mt. 25 (1887) 14-. 

 , , geometrical proof. Vries, J. de. Amst. 



Ak. Vs. 5 (1897) 218-. 

 , , obtained by differentiation. Rogel, F. 



Arch. Mth. Ps. 10 (1891) 209-. 

 , , problems. Bougaieff, N. V. N. A. 



Mth. 13 (1874) 381-. 

 T , ., series giving relation between. Minin, 



A. P. Mosc. S. Sc. Bll. 83 (No. 1) (1893) 



23-. 



,, theory. Cantor, G. Gott. Nr. (1880) 161-. 

 Generating Junction, numerical, of binary 



seventhic. Cayley, A. Am. J. Mth. 2 (1879) 



71-. 



functions in theory of numbers, class. 

 MacMahon, P. A. [1893] Phil. Trans. (A) 



. 185 (1895) 111-. 



Greatest integer in certain series. Cesdro, E. 



[1882] Liege S. Sc. Mm. 10 (1883) (No. 6) 



355 pp. 



integers. Gegenbauer, L. Wien Ak. Sb. 

 94 (1887) (Ab. 2) 611-. 



. Busche,E. CrelleJ. Mth. 103 (1888) 118-. 



, sums. Hacks, J. ActaMth. 10 (1887) 1-. 



, . Mathews, G. B. L. Mth. S. P. 31 



(1900) 355-. 

 , , in arithmetical progressions. Zeller, 



C. Gott. Nr. (1879) 243-. 

 , theorem. Schubert, H. [1895] Hamb. 



Mth. Gs. Mt. 3 (1900) 223-. 

 , (Schubert). Busche, E. [1895] 



Hamb. Mth. Gs. Mt. 3 (1900) 225-. 

 Identities, numerical, application to theory of 



numerical functions. Baskakov, S. I. 



[1881] (xn) Eec. Mth. (Moscou) 10 (1882- 



83) (Pt. 1) 313-. 

 , , Liouville's, deduced from Bugaev's 



theorem. Sokolov, D. N. [1891] Eec. Mth. 



(Moscou) 16 (1893) 89- ; Fschr. Mth. (1891) 197. 

 , a source of. Ocagne, M. d'. Par. S. Mth. 



Bll. 15 (1887) 133-. 



230 



