4040 



Elliptic and Single Theta Functions 



4040 



integration by. Bouquet, J., & Briot, . 



C. B. 61 (1855) 1229-. 

 . Dolbnia, I. Kazan S. Ps.-Mth. Bll. 1 



(1891) 46-; Fschr. Mth. (1891) 463-. 



of equation connected with. MacMahon, 

 P. A. B. A. Bp. (1882) 450-. 



interpolation problem. Appell, P. Bll. Sc. 



Mth. 10 (1886) 109-. 

 . Schottky, F. Crelle J. Mth. 107 (1891) 



189-. 

 inverse. Cayley, A. Camb. Mth. J. 4 (1845) 



257-. 

 , integrals expressed by. Greenhill, A. G. 



Camb. Ph. S. P. 3 (1880) 361-. 

 investigations. Klein, F. Mth. A. 26 (1886) 



455-. 

 involved in definite integrals. Glaisher, 



J. W. L. B. S. P. 29 (1879) 331-. 

 system of integrals. Glaisher, J. W. L. 



QJ. Mth. 19 (1883) 145-. 

 Jacobian. Stringham, I. A. Mth. 8 (1893-94) 



105-. 

 of 1st kind. Serret, J. A. Liouv. J. Mth. 8 



(1843) 145-. 

 . Iaggi,E. N. A. Mth. 17 (1898) 367-. 



, fundamental properties, geometric 

 explanation. Lemeray, E. M. N. A. Mth. 

 19 (1900) 255-, 289-. 



, geometric demonstration of two 

 theorems. SchlSfii, L. Grunert Arch. 12 

 (1849) 188-. 



, study. Leaute, H. Par. EC. Pol. 



J. Cah. 46 (1879) 65-. 



- , Jacobi's 1st and 2nd theorems, 

 supplements to. Essen, E. Grunert Arch. 

 21 (1853) 241-, 418-. 



i representation by arcs of curves. 

 Allegret, \A.] C. B. 70 (1870) 1032-. 



, gauche biquadratics. Leaute, 



H. C. B. 83 (1876) 527-. 

 , , geometric. Roberts, W. Liouv. 



J. Mth. 8 (1843) 263-. 

 , , . Serret, J. A. Camb. and 



Dubl. Mth. J. 1 (1846) 187-. 

 , , . Davidov, A. Y. (xii) Bee. 



Mth. (Moscou) 2 (1867) (Pt. 1) 129-. 

 and 2nd kinds. Lobatto, R. Amst. N. 



Vh. 12 (1846) 119-. 

 . Bellavitis, G. Padova Bv. 



Period. 1 (1851-53) 149-. 

 . Kupper, G. Crelle J. 55 



(1858) 89,-. 



, as functions of amplitude. 



Liouville, J. [1833] Par. EC. Pol. J. 23 cah. 

 (1834) 37-. 



, modulus. Liouville, J. 



Liouv. J. Mth. 5 (1840) 34-, 441-. 



2nd kind. Frobenius, G. [1881] Crelle J. 

 Mth. 93 (1882) 53-. 



and 3rd kinds, expansion in trigonometric 



series. Krause, M. Mth. A. 30 (1887) 425-, 

 516- ; 33 (1889) 108- ; 35 (1890) 577-. 



, results in. Griffiths, J. B. S. 



P. 38 (1885) 206-, 316-. 



3rd kind. Salvert, (le vicomte) de. 

 . Brux. S. Sc. A. 21 (1897) (Pt. 2) 131-. 



i calculation, method. Somoff, J. 

 Crelle J. 47 (1854) 269-. 



of 3rd kind, reduction to functions of two 



arguments. Verhulst, P. F. Quetelet Cor. 



Mth. 11 (1839) 225-. 

 , representation, geometric. Tortolini, 



B. G. Arcad. 100 (1844) 257-. 

 , , . Drobisch, M. W. Grunert 



Arch. 24 (1855) 320-. 

 logarithm, behaviour. Schottky, F. Crelle J. 



Mth. 108 (1891) 342-. 

 method, short. Meech, L. W. Des Moines 



Anal. 4 (1877) 129-, 161- ; 5 (1878) 9-. 

 , (Meech). Kummell, C. H. Des Moines 



Anal. 5 (1878) 17-, 97-. 

 modulus, formulas relative to. Hermite, C. 



Liouv. J. Mth. 9 (1864) 313-. 



as function of quotient of two periods. 

 Hermite, C. A. Mt. 3 (1869-70) 81-. 



numerators and denominators satisfying partial 



differential equation. Jacobi, C. G. J. Crelle 



J. 36 (1848) 81-. 

 of 2nd order. Bricard, R. Par. S. Mth. Bll. 



25 (1897) 212- ; 26 (1898) 91-. 

 , properties. Berger, A. Ups. S. Sc. 



N. Acta 14 (1891) No. 12, 50 pp. 



3rd order, differential equation. Pfannen- 

 stiel, E. Ups. S. Sc. N. Acta 15 (1895) 

 No. 3, 18 pp. 



nth order. Rados, G. Mth. Termt. Ets. 6 



(1888) 353-. 



and orthogonal transformations. Wilkinson, 

 M. M. U. L. Mth. S. P. 14 (1882-83) 

 203-. 



periodicity. Benthem, A. N. Arch. Wisk. 3 

 (* 1877) 186-. 



, double. Franklin, F. Am. J. Mth. 11 



(1889) 283-. 



periods, existence of two. M6ray, C. Par. EC. 



Norm. A. 1 (1884) 177 r . 

 and their powers, expansion. Andre, D. C. B. 



83 (1876) 135-. 

 , in series. Andre, D. Par. EC. 



Norm. A. 6 (1877) 265-. 

 property, demonstration. Walton, W. [1870] 



QJ. Mth. 11 (1871) 177-. 

 and g-series. Glaisher, J. W. L. Mess. Mth. 



13 (1884) 126-. 



quadriquadric curve. Cayley, A. Mth. A. 25 

 (1885) 152-. 



of nth rank. Klein, F. Leip. Mth. Ps. B. 36 



(1884) 61-. 

 rational combinations. Meyer, C. O. [1885] 



Crelle J. 56 (1859) 314-. 

 and reciprocal factorials. Cauchy,A.L. C.B. 



17 (1843) 825-. 

 recurring relation. Jonquieres, E. de. C. B. 



101 (1885) 415-. 

 reduction of some definite integrals to, and 



applications. Tortolini, B. G. Arcad. 116 



(1848) 137-, 265-. 

 integrals to. Dienger, J. Grunert Arch. 



11 (1848) 94-; 13 (1849) 424-. 



. Tortolini, B. Tortolini A. 3 

 (1860) 183-. 



, cases. Sparre, (le comte) de. 



Brux. S. Sc. A. 8 (1884) (Pt. 2) 97-; 9 (1885) 

 (Pt. 2) 205- ; 21 (1897) (Pt. 2) 45-. 



representation. Liouville, J. C. B. 21 (1845) 

 1255-. 



316 



