4040 



Elliptic and Single Theta Functions 



4040 



4 dx, Euler's reduction to integral of 



rational function. Hermite, C. Liouv. J. 



Mth. 6 (1880) 5-. 

 , (Hermite). Bounia- 



kowsky, V. St Pet. Ac. Sc. Bll. 26 (1880) 



188-. 

 E and F, indefinite integrals containing. 



Bierens de Haan, D. B. A. Bp. (1883) 440-. 

 dx/JY, transformation. Stieltjes, T. J. Toul. 



Fac. Sc. A. 2 (1888) K, 26 pp. 



Elliptic integration. Raivson, R. B. A. Bp. 

 (1849) (Pt. 2) 4-. 



series, approximate evaluation by algebraic 

 means. Cesdro, E. Mathesis 14 (1894) 

 177-. 



-transcendent identities, theorems in theory 

 of numbers deduced from. Glaisher, J. W. L. 

 B. A. Bp. 43 (1873) (Sect.) 10-. 



relations. Glaisher, J. W. L. B. A. 



Bp. (1874) (Sect.) 15-. 



transcendents, representation of functions 

 by. Hermite, C. [1880] A. Mt. 10 (1880-82) 

 137-. 



Equations algebraically integrable. Euler, L. 

 [1778] St Pet. Ac. Sc. N. Acta 13 (1802) 3-. 



containing both algebraic and transcendental 

 functions, principle for simplification. 

 Zehfuss, G. Schlomilch Z. 5 (1860) 210-. 



Euler's equation. Laguerre, E. (x) Par. S. 



Phlm. Bll. 7 (1871) 270. 

 . Stieltjes, T. J. Bll. Sc. Mth. 12 



(1888) 222-; C. B. 107 (1888) 617-. 

 . Jamet, V. Bll. Sc. Mth. 19 (1895) 



208-. 

 . Lacour, E. N. A. Mth. 18 (1899) 



293-. 

 , forms of integral. Laguerre, E. Par. 



S. Mth. Bll. 3 (1875) 101-. 

 , , case. Hadamard, J. Bll. 



Sc. Mth. 20 (1896) 263-. 

 , integration of an equation analogous to. 



Picard, E. C. B. 92 (1881) 506-. 

 , by lines of curvature of ruled hyper- 



boloid. Floquet, G. N. A. Mth. 14 (1875) 



120-. 

 , (Floquet). 



Escary, . N. A. Mth. 15 (1876) 61-. 



and lines of curvature of ellipsoid. 

 Adam, P. Par. S. Mth. Bll. 22 (1894) 

 205-. 



Expansion of sin x and cos x in infinite series of 

 factors. Duhamel, J. M. C. Liouv. J. Mth. 

 19 (1854) 121-. 



2K 



sin and cos of n am re in trigono- 

 metric series. Lindeberg, K. M. Stockh. 

 Ofv. 32 (1875) No. 8, 31-. 



snx. Harris, R. A. A. Mth. 4 (1888) 



87-. 

 GjK, KjG, IjE,... in ascending powers 



of fc 2 . Glaisher, J. W. L. Mess. Mth. 19 



(1890) 164-. 

 Expansions in powers of fc' 2 -fc 2 . Glaisher, 



J. W. L. Mess. Mth. 22 (1893) 109-. 



Expansions in series and application to elliptic 

 functions. Schlomilch, 0. [1854] Leip. Ab. 

 Mth. Ps. 2 (1855) 395-. 



of theta functions in powers of argument. 

 Glaisher, J. W. L. Camb. Ph. S. P. 

 6 (1889) 96-. 



\(x), p{x) and their powers, with 

 regard to modulus. Andre, D. Par. S. Mth. 

 Bll. 6 (1878) 163- ; Par. EC. Norm. A. 8 

 (1879) 151- ; 9 (1880) 107-. 



K', E', J', G' in powers of modulus. 

 Glaisher, J. W. L. Camb. Ph. S. P. 

 5 (1886) 184-, 232-. 



K, I, G, E in powers of k' 2 -K*. 

 Glaisher, J. W. L. Mess. Mth. 19 (1890) 146-. 



Formula of G. Fontene. Hermite, C. Bll. 



Sc. Mth. 20 (1896) 218-. 

 Hermite. Lipschitz, . Crelle J. Mth. 



100 (1887) 66-. 



KE' + K'E-KK' = ?. Glaisher, J. W. L. 



[1874] Mess. Mth. 4 (1875) 95-. 

 Formulae of Jacobi's on functions of k, k', K, K' 



in q series. Glaisher, J. W. L. Mess. Mth. 



5 (1876) 174-. 

 , systems for sn, en, dn of u + v + w. Johnson, 



W. W. L. Mth. S. P. 13 (1881-82) 97-. 



for sn 8u, en 8u, dn 8w, in terms of sn u. 

 Glaisher, E. H. B. S. P. 32 (1881) 444; 

 33 (1882) 480-. 



sn, en, dn of u + v + w. Glaisher, J. W. 



L. [1881] Mess. Mth. 11 (1882) 45-. 

 Functional images in Cartesians. Greenhill, 



A. G. QJ. Mth. 18 (1882) 231-, 346-. 

 Functions having algebraic addition theorem. 



Pszeborski, A. G. Fschr. Mth. (1896) 341-. 

 G-function, theory. Barnes, E. W. QJ. 



Mth. 31 (1900) 264-. 

 General elliptic element, transformations. 



Russell, R. L. Mth. S. P. 18 (1886-87) 48-. 

 integral, integration. Lobatto, R. Crelle 



J. 10 (1833) 280-. 

 Geometrical application of a theorem of Jacobi. 



Humbert, G. Liouv. J. Mth. 1 (1885) 347-. 

 Gudermannian of u. Cayley, A. Ph. Mg. 



24 (1862) 19-. 

 Hermite 's H-product theorem. Cayley, A. 



Mess. Mth. 18 (1889) 104-. 

 Higher transcendents in mechanical problems. 



Russell, W. H. L. Mess. Mth. 7 (1878) 18-, 



136- ; 8 (1879) 8-; 9 (1880) 40-. 

 Infinite series, exponents of which are con- 

 tained in two quadratic forms. Jacobi, C^ 



G. J. Crelle J. 37 (1848) 61-, 221-. 

 Integral of 



dx 



dy 



MacMahon, P. A. C. B. 95 (1882) 831-. 

 Integrals of differential equations, satisfied by 



moduli of elliptic integrals. Fuchs,L. [1876] 



Crelle J. Mth. 83 (1877) 13-. 

 form \/l +p sin% . cos 2 a; etc. Bierens de 



Haan, D. Amst. Ak. Vh. 21 (1881) (No. 6) 



50pp. 



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