3630 Expansions in Series 



Bernoulli's functions, generalised, applications. 



ImSeneckij, V. G. [1885] St Pet. Ac. Sc. Mm. 



(Rs.) 52 (1886) (Suppl.) No. 2, 62 pp. ; Fschr. 



Mth. (1886) 373-. 

 polynomials and their applications. Sonine, 



N. J. Fschr. Mth. (1888) 424. 

 Cases. Deruyts, J. Brux. Mm. Cour. 4, 47 



(1886) No. 6, 18 pp. 

 Convergence - subtrahends for trigonometric 



functions expressed in infinite sums. 



Boliannan, E. D. A. Mth. 1 (1884-85) 49-. 

 Deduction of C, S, from 



c+is= s 7i -V 1 ^>*. 



x=0 *1 C x 



Pdnek, A. Casopis 17 (1888) 227-; Fschr. 

 Mth. (1888) 263. 

 Determination of coefficients in 



(n, 2) + ... 



where f(n) = A l <j>(n, \} + A z <j>(n, 2) + ... 



and f (n, k) = a 1 cf> (n, 1) + 0^ (n, 2) + .... 



Minin, A. P. Eec. Mth. (Moscou) 13 (1886) 



535-; Fschr. Mth. (1887) 173-. 

 Effective validity, cases. Pincherle, S. Em. 



E. Ac. Line. Ed. 5 (1896) (Sem. 1) 27-. 

 Expansion in continued fractions. Hurwitz, A. 



Acta Mth. 11 (1887-88) 187-. 

 -- denominators of convergents of continued 



fraction. Rouche, E. Par. EC. Pol. J. 



37" eah. (1858) 1-. 

 -- Euler's functions. Rogel, F. Prag Sb. 



(1896) (Mth.-Nt.) No. 42, 9pp. 

 -- factorials. Schldmilch, 0. Leip. B. 15 



(1863) 58-. 

 --- of the variable. Graves, C. Ir. Ac. P. 



3 (1847) 455-. 



harmonic functions. Steklov, V. A. 

 Kharkov Mth. S. Com. 5 (1896?) 60-; Fschr. 

 Mth. (1896) 203- ; C. E. 128 (1899) 279-. 



-- infinite series. Morera, G. Tor. Ac. Sc. 



At. 21 (1885) 892-. 

 -- inverse factorial series. Kluyver, J. C. 



N. Arch. Wisk. 4 (1899) 74-; Fschr. Mth. 



(1899) 372. 

 -- other functions. Hugoniot, . C. E. 



95 (1882) 907-. 

 ---- (Hugoniot). DM Bois-Reymond, P. 



C. E. 96 (1883) 61-. 



--- , form of residue. Lagrange, C. 

 C. E. 98 (1884) 1422-. 



, any number of variables. 

 Lagrange, G. Brux. Mm. Cour. 4, 48 (1886) 

 No. 2, 16 pp. 



-- polynomials. Pincherle, S. C. E. 107 



(1888) 986-. 



. Lean, L. Par. S. Mth. Bll. 27 



(1899) 194-. 

 -- powers of n algebraic functions from n 



equations. Arzela, C. G. Mt. 11 (1873) 



368-. 

 ---- a polynomial. Jacobi, C. G. J. 



[1847] Crelle J. 53 (1857) 103-. 

 ------ e Laguerre, E. [1878-79] 



C. E. 86 (1878) 383-; Crelle J. Mth. 88 (1880) 



Multivariable Functions 3640 



Expansion in trigonometric functions of im- 

 aginary arcs. Clapeyron, E., & "Lame, G. 

 Crelle J. 6 (1830) 45-. 



trigonometric functions sin^a;, cos*>x, x p 



when p is irrational. Yakovlev, N. Y. (xn) 

 Kazan Un. Mm. (1857) (Bk. 4) 84-. 



Formula of Darboux. Mansion, P. Brux. S. 

 Sc. A. 13 (1889) (Pt. 2) 108-. 



Hermite. Pincherle, S. Em. E. Ac. 



Line. Ed. 1 (1885) 267-. 



Functions of fractional powers of sine and 

 cosine. Stein, J. P. Gergonne A. Mth. 15 

 (1824-25) 150-. 



one real variable, expansion in Jacobian 



functions. Dini, U. A. Mt. 10 (1880-82) 

 145-. 



Generating functions, fundamental theorem. 

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

 (Trida 2) 1 (1892) Art. 33, 7pp.; Fschr. Mth. 



Holomorphic function within a given contour, 



expansion in polynomials. Renaux, . C. 



E. 129 (1899) 473-, 626. 

 Integral function, expansion in denominators 



of certain regular continued fractions, pro- 



perty of. Gegenbauer, L. Wien Ak. Sb. 98 



(1890) (Ab. 2a) 867-, 

 Lagrange's series, generalisation. Amigues, E. 



C. E. 116 (1893) 368-, 429. 

 -- , series analogous to. Amigues, E. C. E. 



99 (1884) 1149-. 

 -- , --- . Bougalev, N. C. E. 131 



(1900) 793-. 

 Series with imaginaries. Denzler, W. Zur. 



Vjschr. 1 (1856) 333-. 

 of rational functions. Borel, E. C. E. 130 



(1900) 1061-. 

 Uniform functions, expansion in polynomials. 



Painleve; P. C. E. 102 (1886) 672-; 129 



(1899) 27-. 

 Wronski's law, elementary demonstration. 



Lagrange, C. Brux. Mm. Cour. 4, 47 (1886) 



No. 2, 8 pp. 

 (x - z) m , expansion in powers of (z 2 1). 



Laguerre, E. C. E. 86 (1878) 956-. 

 /(#), expansion in series 



35-. 



. Humbert, G. Par. S. Mth. 



Bll. 8 (1880) 124-. 



Rogel, F. Prag Sb. (1892) (Mth.-Nt.) 3-. 



*, expansion in powers of sin x. Gomes 



Teixeira, F. N. A. Mth. 15 (1896) 270-. 



3640 Functions of several 

 variables. 



Trzaska, W. Par. T. Nauk Sc. Pam. 2 (*1872) 



27-; Bll. Sc. Mth. As. 6 (*1874) 156. 

 Mittag-Leffler, G. Stockh. Ofv. 34 (1877) No. 



10, 3-, 17-. 

 (Mittag-Leffler.) Weierstrass, C. T. W. Berl. 



Ak. Mb. (1880) 707-. 

 ( -- .) Hermite, C. [1881] Crelle J. Mth. 



92 (1882) 145-. 



Combescure, E. C. E. 96 (1883) 235-, 483-. 

 Cousin, P. Acta Mth. 19 (1895) 1-. 

 Lebesgue, H. C. E. 128 (1899) 811-. 



298 



