3220 



Infinite Products 



3220 



(y 

 1 



- etc., note. Brisse, 

 C. N. A. Mt^ 16 '(1877) 418-. 



Hermite, C. (xn) Mathesis 

 (1881) 37. 



. Baehr, G. F. W. (xn) Mathesis 1 (1881) 58. 

 . Catalan, E. C. (xn) Mathesis 1 (1881) 58. 



f (x) = f (0) + . . . x ( x ~" n ~ 1 fW ( n p) . . . (Abel) . 



Halphen, G. C. R. 93 (1881) 1003- ; Par. 

 S. Mth. Bll. 10 (1882) 67-. 

 2jB>/w, Buniakoff sky's formula. Petr, K. 

 (Sasopis 16 (1887) 169- ; Fschr. Mth. (1887) 

 172-. 



"2^. Jonquiere, A. Par. S. Mth. Bll. 17 



n=l " 



(1889) 142-. 



2 p and 2 ^ . Markoff, A. C. R. 109 (1889) 

 934-. 



i-()= 1 ZY-Y. Piltz,. D. Nf. Vh. (1891) 



/TO-S^W 



(In. 2) 15-. 



2n-. Lafay, A. Toul. Fac. Sc. A. 6 (1892) 



x-2q) n + ... +rand x n - (x - q) 

 r, J. W. 



I, 6 pp. 

 x+(x- 



+ (x- 2q) n - . . . r, values. Glaisher 



L. QJ. Mth. 31 (1900) 193-. 

 1" (x - l)+2(a?- 2)*+ ... . Glaisher, J. W. L. 



QJ. Mth. 31 (1900) 241-. 



INFINITE PRODUCTS. 



Racagni, G. Mil. Mm. I. Lomb. Yen. 1 (1812- 



13) 59-, 341-. 

 Le Francois, (Prof.) . Brux. Mm. Cour. 4, 



14 (1841) 71 pp. 



Schlomilch, 0. [1851] Crelle J. 44 (1852) 344-. 

 Weierstrass, C. [1854] Crelle J. 51 (1856) 1-. 

 Dini, U. [1868] A. Mt. 2 (1868-69) 28-. 

 Rodrigues, J. M. G. Teix. J. Sc. 3 (1881) 87-. 

 Arzela, C. Bologna Ac. Sc. Mm. 4 (1882) 419- ; 



Bologna Rd. (1885-86) 92-. 

 Giudice, F. G. Mt. 28 (1890) 305-, 380. 

 Chessin,A. S. J. H. Un. Cir. [15 (1895-96) ]38-. 

 Anissimow, W. A. Fschr. Mth. (1897) 221. 

 Pasquale, V. de. G. Mt. 35 (1897) 259-. 

 Application of calculus of residues. Anon. 



Ferussac Bll. Sc. Mth. 12 (1829) 202-. 

 . Cauchy, A. L. C. R. 17 



(1843) 572-. ' 



Case. Gill, C. Mth. Misc. 2 (1839) 140-. 

 Constant G and some products. Catalan, E. 



Brux. Ac. Mm. 51 (1893) (No. 2) 28 pp. 

 Convergence. Arndt, F. Grunert Arch. 21 



(1853) 78-. 



. Pringsheim, A. Mth. A. 33 (1889) 119-. 

 . Bruno de Cabedo, J. G. Teix. J. Sc. 10 



(1891) 138-. 

 , conditional. Pringsheim, A. Mth. A. 44 



(1894) 413-. 

 Decomposition of functions into factors. 



Cauchy, A. L. C. R. 19 (1844) 1069- ; 



30 (1850) 186-. 

 numbers into infinite products. Cantor, G. 



Z. Mth. Ps. 14 (1869) 152-. 



Decomposition of numbers into infinite pro- 

 ducts (Cantor). Gegenbauer, L. Mh. Mth. 

 Ps. 3 (1892) 87-. 



Elementary theory. Genocchi, A. N. A. Mth. 

 8 (1869) 121-. 



Expansion. Rogers, L. J. [1893-94] L. 

 Mth. S. P. 24 (1893) 337-; 25 (1894) 318- ; 

 26 (1895) 15-. 



by Euler. Glaisher, J. W. L. [1879] Mess. 

 Mth. 9 (1880) 45-. 



of functions in infinite products. Bock, J. W. 

 Hamb. Mth. Gs. Mt. 1 (1889) 76-. 



in series, proof. Sylvester, J. J. (xn) J. 

 H. Un. Cir. [2] (1883) 46. 



Finite product and infinite product, relation. 



Schlomilch, 0. Grunert Arch. 3 (1843) 442-. 

 Formula of Cauchy. Cazzaniga, P. Mil. I. 



Lomb. Rd. 15 (1882) 273-. 

 Holomorphic function, special mode of re- 

 solution into infinite product. Kotelov, K. I. 



Kazan S. Nt. (Ps.-Mth.) P. 7 (1889) 407- ; 



Fschr. Mth. (1890) 396. 

 Interpolation of two products. Ivanov, I. I. 



Kharkov Mth. S. Com. 1 (1889) 78- ; Fschr. 



Mth. (1888) 423-. 

 Numerical product, case. Glaisher, J. W. L. 



[1876] Mess. Mth. 6 (1877) 71-, 189-. 

 Power series for a certain product. Schrdder, 



J. [1897] Hamb. Mth. Gs. Mt. 3 (1900) 



302-. 

 Products arising from linear equation. Cauchy, 



A. L. C. R. 17 (1843) 523-, 567-. 



developable in powers of - . Giudice, . 



Palermo Cir. Mt. Rd. 5 (1891) 287-. 



and divisors of numbers, theorem derived 

 from Euler's. Dienger, J. Crelle J. 40 

 (1850) 235-. 



expressing real functions with infinitely 

 close zeros. Broden, T. Mth. A. 51 (1899) 

 299-. 



roots of integers, properties. Schaar, M. 



Brux. Ac. Bll. 16 (1849) 580-. 

 a number. Schaar, M. Brux. Ac. 



Bll. 13 (1846) 228-. 



and powers of a number. Le 

 Francois, (Prof.) . Brux. Ac. Bll. 19 (1852) 

 23-. 



and series, changes in values due to changes 

 in order of terms. Casorati, F. Mil. I. 

 Lomb. Rd. 1 (1868) 126-. 



, evaluation. Mildner, R. [1883] (x) 



Wien Ak. Sb. 88 (1884) (Ab. 2) 591-. 



of series of factors. Dobinski, G. Arch. 

 Mth. Ps. 59 (1876) 98- ; 61 (1877) 434-. 



Properties and calculation. Savinov, A. (xn) 



Kazan Un. Mm. (1851) (Bk. 4) 43-. 

 Reduction in series. Novi, G. G. Mt. 2 (1864) 



1-, 40-. 

 Relation between two products. Eisenstein, G. 



Crelle J. 27 (1844) 285- ; 28 (1844) 36-. 

 Semi-convergent products. Catalan, E. C. 



[1871-86] Brux. Ac. Sc. Mm. 40 (1873) 



(No. 2) 127 pp. ; Liege S. Sc. Mm. 13 (1886) 



151-, 254-. 

 . Beaupain, J. Brux. Mm. Cour. 4, 



53 (1893-94) No. 7, 8 pp. 



252 



