3220 



Infinite Series 



3220 



Expansion, continued. 



semi-convergent, case. Sonin, N. Ja. [1891] 



Vars. S. Nt. Tr. (1891-92) (G. R., Ps. C.) 



No. 3, 3-; Fschr. Mth. (1892) 232. 

 , . Lerch, M. Prag Ceske Ak. Fr. 



Jos. Ez. (Tfida 2) 5 (1896) Art. 18, 6 pp. ; 



Fschr. Mth. (1896) 207. 

 , general form. Sonin, N. Ja. [1891] 



Vars. S. Nt. Tr. (1891-92) (G. R., Ps. C.) 



No. 4, 2-. 

 and summation, cases. Winckler, A. Wien 



Ak. Sb. 64 (1871) (Ab. 2) 799-. 

 symbolic versus operative, case. Hathaway, 



A. S. Des Moines Anal. 5 (1878) 38-. 

 theorem of Cauchy. Lamarle, E. Brux. Ac. 



Bll. 13 (1846) 520-. 

 , general. Schlomilch, O. Grunert Arch. 3 



(1843) 400-. 

 theorems. Faa de Bruno, F. [1880] Crelle J. 



Mth. 90 (1881) 186-. 



. McClintock,E. Am. J. Mth. 4 (1881) 16-. 

 theory. Knar, J. Baumgartner Z. 2 (1827) 



254-, 366-. 

 . Tetmajer, J. (xn) Krk. Ak. (Mt.-Prz.) 



Pam. 3 (1877) 155- ; 4 (1878) 1-. 

 of transcendental functions, cases. Trudi, N. 



Nap. At. I. Inc. 4 (1867) 105-. 

 trigonometric. Rogel, F. Prag Sb. (1892) 



(Mth.-Nt.) 273-. 

 in two different series of powers, comparison. 



Gopel, A. Grunert Arch. 6 (1845) 25-. 

 uniform, of all positive quantities less than 



unity. Lilroth, J. [1882] Mth. A. 21 (1883) 



use of complementary variables. Cauchy, A. L. 



C. E. 20 (1845) 280-. 

 without use of derivatives. [1895] Echols, 



W. H. A. Mth. 10 (1895-96) 17-. 

 of (l + x) m , Euler's. Catalan, E. C. Liouv. 



J. Mth. 9 (1844) 161-. 

 - {(x - xj* +(y- ytf + ('- *!) 2 } -*. Plana, 



G. G. Arcad. 104 (1845) 182-. 

 f(y) -f( x )> i n powers of y -x. Levanen, S. 



Helsingf. Ofv. 17 (1875) 1-. 

 F(x), expansion of derivatives in powers of 



index of derivative. Griinwald, A. C. Prag 



Sb. (1880) 276-; Prag Ab. (1882) No. 2, 



63pp. 



of (Sa r r )~ 1 (a =l), in powers of x. Gam- 

 bioli, D. [1891] Bologna Ed. (1891-92) 39-. 



Finite expressions for infinite series. Dienger, 



J. Crelle J. 34 (1847) 209-. 

 Formula. Glaisher, J. W. L. Mess. Mth. 5 



(1876) 164-. 

 Functions ' ' differing as little as possible from 



zero." Tchebitchef, P. L. Liouv. J. Mth. 



19 (1874) 319-. 

 General problem, solution, Andre, D. C. E. 



92 (1881) 697-. 

 solution of algebraic problems by series. 



Marron, F. [1850] Madrid Mm. 2 (1853) 233-. 

 Geodetic positions on spheroid, formulae, ex- 

 pansion. Andrce, . Kjob. Ov. (1859) 27- ; 



As. Nr. 50 (1859) 161- ; 53 (1860) 369-. 



Geometric representation. Popper, J. Wien 

 Az. 1 (1864) 34-. 



series of second order. Hochheim, A. 

 Magdeb. Nt. Vr. Jbr. u. Ab. (1886) 127- ; 

 (1887) 25-. 



Harmonic series. Kinkelin, H. [1861] Basel 



Vh. 3 (1863) 18-. 

 . Knar, J. Arch. Mth. Ps. 41 (1864) 



297-; 43 (1865) 134-. 

 . Simon, H. Arch. Mth. Ps. 8 (1890) 



113- ; 9 (1890) vn. 

 , properties, with table. Hill, C. J. D. 



Lund. Acta Un. 3 (1866) (Mth.) No. 1, 



16 pp. 



and Stirling's formula. Mansion, P. 

 (xn) Mathesis 1 (1881) 169-. 



Higher series, new forms. Lukas, F. C. [1881] 



Arch. Mth. Ps. 67 (1882) 327-. 

 Identities. Glaisher, J. W. L. [1875] Mess. 



Mth. 5 (1876) 111-. 

 Indeterminate coefficients. Wittstein, T. 



Grunert Arch. 3 (1843) 300-. 

 . Schlomilch, O. Grunert Arch. 3 (1843) 



269-. 

 (Schlomilch). Barfuss, F. W. Grunert 



Arch. 4 (1844) 225-. 

 (Barfuss). Schlomilch, 0. Grunert Arch. 



5 (1844) 374-. 

 (Schlomilch). Barfuss, F. W. Grunert 



Arch. 7 (1846) 29-. 



, extension of theory. Pexider, J. Casopis 

 28 (1899) 277-; Fschr. Mth. (1899) 240. 



Integrability, case. Arzela, C. Em. E. Ac. 



Line. Ed. 1 (1885) 321-. 

 Integral and integro-geometric series. Roe, 



E. D. [1896] A. Mth. 11 (1896-97) 184-. 



series. Hadamard, J. [1897] Acta Mth. 22 

 (1899) 55-. 



with several variables. Lemaire, E. Bll. 



Sc. Mth. 20 (1896) 286-. 

 Integration. Schlomilch, 0. Grunert Arch. 



3 (1843) 278-. 

 . Du Bois-Reymond, P. Berl. Ak. Sb. (1886) 



359-. 

 . Fiske, T. S. N. Y. Am. Mth. S. Bll. 3 



(1897) 223-. 



Inversion. Cesdro, E. A. Mt. 13 (1885) 339-. 

 . JeHek, 0. Wien Ak. Sb. 99 (1891) (Ab. 2a) 



191-. 

 . Zorawski, K. Prace Mt.-Fiz. 5 (1894) 



146- ; Fschr. Mth. (1893-94) 393-. 

 Inversions of terms of given infinite series, and 



analytic representation of result. Pringsheim, 



A. Mth. A. 38 (1891) 153- . 

 Irrationality. Stern, M. A. Crelle J. Mth. 



95 (1883) 197-. 



of value, cases. Stern, M. A. Crelle J. 

 37 (1848) 95-. 



2m 1 



Limit of S - for m =00. Unferdinger, F. 



Arch. Mth 1 . Ps. 47 (1867) 231- ; Wien Ak. 

 Sb. 55 (1867) (Ab. 2) 93-. 

 r=m (n-1) 



S (m+rS) e for m=oo. Unfer- 

 dinger, T F] Wien Sb. 57 (1868) (Ab. 2) 621-. 



Limited series, remainders. Cauchy, A. L. C. 

 E. 34 (1852) 156-. 



244 



