2910 



Special Numbers and Numerical Functions 



2910 



Inverse arithmetical functions. Cesdro, E. 



G. Mt. 23 (1885) 168-. 

 Laisant's function Z(l+\/2), calculation. 



Seydler, A. Casopis 20 (1891) 89-; Fschr. 



Mth. (1891) 442. 

 , , new formula. Studnicka, F. J. 



Casopis 20 (1891) 66- ; Fschr. Mth. (1891) 



441. 

 Mean and asymptotic expressions in arithmetic. 



Cesdro, E. G. Mt. 25 (1887) 1-. 



values of certain numerical functions. La 

 Vallee-Poussin, de. Brux. S. Sc. A. 22 

 (1898) (Ft. 1) 84-. 



Mobius-Mertens function. Lerch's theorem. 



Dintzl, E. Mh. Mth. Ps. 11 (1900) 67-. 

 Number and sum of divisors of number. 



Hammond, J. Mess. Mth. 20 (1891) 158-, 182-. 

 Numbers with no square factors. Gegenbauer, 



L. Wien Ak. Sb. 100 (1891) (Ab. 2a) 1054-. 



representable by S/ r (x r ). Pascal, E. G. 



Mt. 25 (1887) 45-. * 



=5 (mod. 12), theorem. Liouville, J. 

 Liouv. J. Mth. 14 (1869) 7-. 



Q n given by n?Q n -2 a (3n 2 -3ra+l) Q n _^ 

 + 2 2<x+1 (n-l) 2 Q n _ 2 = 0, theorem of de Jon- 

 quieres, extension. Gegenbauer, L. Wien 

 Ak. Sb. 97 (1889) (Ab. 2a) 82-. 



K r m , properties. Ocagne, M. d\ Am. J. 

 Mth. 13 (1891) 145-. 



Numerical integrals according to divisors. 



Bougaieff, . C. E. 106 (1888) 652-. 

 (Bougaieff). Cesdro, E, C. B. 



106 (1888) 1340-. 

 . Bugaev, N. V. [1889-1900] 



Eec. Mth. (Moscou) 14 (1890) 169- ; 18 



(1896) 1-; 21 (1901) 335-, 499-; Fschr. 



Mth. (1889) 182- ; (1896) 158 ; (1900) 197- ; 



C. B. 119 (1894) 1259-. 



(Bougaieff, C. B. 1894) . Gegen- 

 bauer, L. Mh. Mth. Ps. 6 (1895) 208. 

 -. , numerical series connected with. Minin, 



A. P. [1877] (xii) Bee. Mth. (Moscou) 9 



(1878-81) (Pt. 1) 128-. 

 Partition of numbers, general law. Bougaieff, 



N. C. B. 100 (1885) 1123-. 



, laws, application to numerical 

 functions. Bougaieff, N. C. B. 100 (1885) 

 1159-. 



Periodic numerical functions, simple. Lucas, 

 E. [1877] Am. J. Mth. 1 (1878) 184-, 289-. 



Series S E 



, calculation. Sylvester, 



J. J. C. B. 50 (1860) 489-. 



E (-\+E[ ) + .... Sylvester, J. J. C. 



w V?/ 



B. 50 (1860) 650-. 



r s" C-V Gcwt, G. Tor. At. Ac. Sc. 5 



(1869-70) 753-. 

 -n~ 



theorem of Syl- 



vester's, generalisation. Gegenbauer, L. 

 Wien Ak. Sb. 94 (1887) (Ab. 2) 757-. 



- 



Series S , summation. Glaisher.J.W.L. 



r =o x + rn 

 Mess. Mth. 24 (1895) 124-. 



2jBp*, theorem. Ivanov, I. St Pet. Ac. 

 Sc. Bll. 2 (1895) 253- ; Fschr. Mth. (1895) 

 218. 



Square roots, arithmetical theorems. Gegen- 

 bauer, L. Wien Ak. Sb. 90 (1885) (Ab. 2) 



395. 

 Sum of like powers of numbers in arithmetical 



progression, and coefficients analogous to 



Bernoulli's. Mollame, V. Catania Ac. 



Gioen. At. 15 (1881) 261-. 

 values of / (x) when x takes TO successive 



values prime to n, theorem of Nasimof. 



Gegenbauer, L. Wien Ak. Sb. 102 (1893) 



(Ab. la) 1265-. 

 Summation of <f> numbers. Perott, J. Bll. 



Sc. Mth. As. 5 (1881) (Pt. 1) 37-. 

 Symbol <j>. Rocquigny, F. [G.] de. Les 



Mondes 48 (1879) 327. 

 Tangent and secant coefficients, independent 



representation. Rogel, F. Arch. Mth. Ps. 



8 (1890) 295-. 

 Totient sums, asymptotic evaluation of certain. 



Lehmer, D. N. Am. J. Mth. 22 (1900) 293-. 

 Totients, two kinds of fcth, and notation for. 



Story, W. E. [1881] (xn) J. H. Un. Cir. 



[1] (1882) 132, 151. 

 Transcendental numerical functions, new. 



Tagliaferro, N. As. Fr. C. B. (1878) 140-. 

 A and T (Kramp). Argand, . Gergonne A. 



Mth. 5 (1814-15) 236-. 

 (n), theorems. Catalan, E. C. Liouv. J. 



Mth. 4 (1839) 7-. 

 . Grunert, J. A. Grunert Arch. 3 (1843) 



196-. 



. Prouhet, E. N. A. Mth. 4 (1845) 75-. 

 . Arndt, F. Crelle J. 31 (1846) 246-. 

 . Oltramare, G. Gen. I. Nt. Mm. 4 (1856) 



1-. 



. Liouville, J. Liouv. J. Mth. 2 (1857) 110- . 

 . Sturm, J. B. Grunert Arch. 29 (1857) 



448-. 

 , theorem, proof. Crone, C. (xn) Ts. Mth. 



4 (1880) 158-. 

 . Rocquigny, F. [G.] de. Les Mondes 51 



(1880) 335-. 

 , and notation of numbers. Eocquigny, 



F. [(?.] de. Les Mondes 54 (1881) 160-. 

 . Catalan, E. C. Li6ge S. Sc. Mm. 15 



(1888) No. 1, 21-. 



= number of divisors of N, value of N. 

 Minin, A. P. [1893] Bee. Mth. (Moscou) 17 

 (1895) 538- ; Fschr. Mth. (1893-94) 277. 



, generalisation. Zsigmondy, K. Crelle J. 



Mth. Ill (1893) 344-. 

 . .Steggall, J. E. A. Edijib. Mth. S. P. 12 



(1894) 23-. 

 , theorems. Moreau, C. N. A. Math. 17 



. Seliwanow, D. F. Fschr. Mth. (1899) 



172. 

 E (x), and reversion of series. Meissel, E. 



Crelle J. 48 (1854) 301-. 

 . Liouville, J. Liouv. J. Mth. 2 (1857) 



231 



