3220 



Infinite Series 



3220 



Series derived from indeterminate equation. 



Oliveira Ramos, J. C. d\ & Faria, C. J. de. 



G. Teix. J. Sc. 7 (1886) 41-; Fschr. Mth. 



(1885) 129-. 

 , each term = sum of two preceding. Clausen, 



P. A. Mth. Ts. 2 (1860) 168-. 

 , exponents of which are contained in two 



quadratic forms. Jacobi, C. G. J. Crelle J. 



37 (1848) 61-, 221-. 



of factorials. Schlomilch, O. Leip. B. 11 

 (1859) 109-. 



, finite or infinite, and series for inverted 

 functions, powers. Buchwaldt, F. Ts. Mth. 

 3 (1885) 65-, 192. 



of functions. Arzela, C. Bologna Bd. 

 (1883) 142-. 



. Pincherle, S. G. Teix. J. Sc. 11 



(1892) 129-. 

 . Arzela, C, Bologna Ac. Sc. Mm. 8 



(1899-1900) 701-. 

 , theorem. Arzela, C. Rm. B. Ac. 



Line. Bd. 1 



term A n (x - a^ (x-aj) ... (x- a n ) , 

 historical note. Enestrom, G. C. R. 103 



523-. 



of geometric means, case. Jarrige, A. 

 [1874] (xn) Isere S. Bll. 5 (1876) 409-. 



integral polynomials representing real 

 functions. Severini, C. Palermo Cir. Mt. 

 Bd. 14 (1900) 157-. 



involving Bernoulli's numbers. Ohm, M. 

 [1825] St Pet. Mm. Sav. Etr. 1 (1831) 

 109-. 



of irreducible fractions. Ocagne, M. d'. 

 Par. S. Mth. Bll. 14 (1886) 93- ; 15 (1887) 

 33-. 



_ _ Kronecker : SS (am 2 + 2bmn + era 2 )-". 

 Franel, . Sch. Nf. Gs. Vh. (1896) 58-. 



and limits. Cockle, (Sir) J. [1875] Mess. 

 Mth. 5 (1876) 25-. 



for log x, a certain. McClintock, E. [1891] 

 Am. J. Mth. 14 (1892) 67-. 



of polynomials. Poincare, H. C. B. 96 

 (1883) 637-. 



, case. Catalan, E. C. [1880] Brux. 



Ac. Sc. Mm. 43 (1882) (No. 10) 40 pp. 



positive terms. Dini, U. G. Mt. 6 

 (1868) 166-. 



. Baillaud, B. Par. EC. Norm. A. 



6 (1869) 185-. 

 . Giudice, F. G. Mt. 28 (1890) 



283-. 

 . Jamet, V. C. E. 114 (1892) 



57-. 

 . Sparre, K. E. Arch. Mth. Ntvd. 



16 (1893) 195-. 

 , including Euler's. Giudice, F. 



G. Mt. 27 (1889) 345-. 

 , sums of coefficients. Tchebycheff, 



P. Acta Mth. 9 (1887) 182-. 

 , . Sonin, N. Ja. [1894] 



St Pet. Ac. Sc. Bll. 2 (1895) 15-; Fschr. 



Mth. (1895) 275-. 



, two theorems. Giudice, . 

 Palermo Cir. Mt. Bd. 4 (1890) 64-. 



proceeding by inverse factorials. Genocchi, 

 A. Tortolini A. 2 (1859) 367-. 



Series and products. Liouville, J. Liouv J. 



Mth. 2 (1857) 438-. 

 , association law. HoSevar, F. Mh. 



Mth. Ps. 5 (1894) 307-. 

 , (Hocevar). Peano, . Mh. 



Mth. Ps. 6 (1895) 204. 



, theorems and proofs. Jensen, 

 J. L. W. V. (xn) Ts. Mth. 5 (1881) 65-. 



of quantities representing number of values 

 of function of n variables, first terms. Cauchy, 

 A. L. C. B. 21 (1845) 1093-. 



reciprocal binomial coefficients. Eogel, 



F. Arch. Mth. Ps. 11 (1892) 412-. 



representing continuous function without 

 derived function (Weierstrass). La Vallee- 

 Poussin, C. de. Brux. S. Sc. A. 16 (1892) 

 (Pt. 1) 57-. 



discontinuous functions, property. 

 Seidel, L. Munch. Ab. 5 (1847) 379-. 



real quantity in given interval. Mollame, 



V. Catania Ac. Gioen. At. 19 (1886) 129-. 



reciprocal of polynomial of nth degree, 

 coefficients. Studnicka, F. J. Casopis 15 

 (1886) 170- ; Fschr. Mth. (1886) 215-. 



simultaneously convergent and divergent. 

 Schlomilch, O. X. Z. Mth. Ps. 26 (1881) 63-. 



solving differential equations. Picart, A. 

 N. A. Mth. 2 (1883) 109-. 



of successive derived functions of function. 

 Pincherle, S. Palermo Cir. Mt. Bd. 11 (1897) 

 165-. 



summable by definite integrals. Schlomilch, 

 O. Grunert Arch. 4 (1844) 23-. 



, terms of which are products of corresponding 



terms of two given series. Durdn Loriga, J. 



Fschr. Mth. (1893-94) 409. 

 , contain binomial coefficients as 



factors. Werner, 0. Grunert Arch. 9 (1847) 



219-. 



for - . Forsyth, A. R. Mess. Mth. 12 



(1883) 142-. 

 Slowly converging series, transformation into 



rapidly converging series. Markoff, A. St 



Pet. Ac. Sc. Mm. 37 (1890) No. 9, 18 pp. 

 Special type of series. Eogel, F. Arch. Mth. 



Ps. 7 (1889) 372-. 

 . Ocagne, M. d'. N. A. Mth. 11 



(1892) 526-. 

 Sum of all negative powers of all integers except 



1 = 1 (Steiner), etc., etc. Stern, M. A. N. 



A. Mth. 8 (1849) 250-. 



fractions of form . r^r , . Stern, 



(2 + x)2+y + l 



M.A. Crelle J. 25 (1843) 280. 



geometrical progression. Young, J. R. 

 Ph. Mg. 28 (1846) 10-. 



. Euzet,. N. A. Mth. 13 (1854) 



301-. 

 reciprocals of square numbers. Enestrom, 



G. Bb. Mth. (1890) 22-. 



series with terms of unlike sign. 

 Studnicka, F. J. fiasopis 17 (1888) 256-; 

 Fschr. Mth. (1888) 256. 



Summation of numerical functions, approxi- 

 mate. Halphen, G. H. C. B. 96 (1883) 

 634-. 



247 



