4040 



Elliptic and Single Theta Functions 



4040 



Integrals, reduction to elliptic forms. Martin, 

 Art. Mess. Mth. 4 (1875) 179- ; 6 (1877) 

 28-; 7 (1878) 24-. 



Integration, complete, of 



x + C dx 



special cases. Buniakovskij , V. St Pet. 

 Ac. Sc. Mm. (Rs.) 3 (*1863) (Suppl.) No. 2, 

 32 pp. 



of irrational fractions. PerevoScikov, D. M. 

 St Pet. Ac. Sc. Mm. (Rs.) 16 (*1870) 1-. 



Integrations over surface of ellipsoid. Tallqvist, 

 . H. Helsingf. Acta 18 (1891) 329-. 



Invariants of $ (u) when -~ = \/ - 7. Kluyver, 



J. C. N. Arch. Wisk. 3 \1898) 36-. 

 Inversion of algebraic integral. Dillner, G. 



Stockh. Ofv. (1885) No. 4, 3- ; Fschr. Mth. 



(1885) 378. 



Jacobian equation. Sterba, J. Crelle J. Mth. 

 , 122 (1900) 198-. 



functions with 1 argument, theory. 

 Brioschi, F. G. Mt. 2 (1864) 8-, 33-, 129-. 



, expansion in powers of variable. 

 Brioschi, F. Tortolini A. 1 (1858) 41-. 



Kleiber's functions K and G. Glaisher, J. W. 



L. Mess. Mth. 22 (1893) 71-. 

 Kronecker's double series (, 77, u, v, w). 



Lerch, M. Mh. Mth. Ps. 5 (1894) 367-. 

 Lambert's series. La Vallee Poussin, C. J. de. 



Brux. S. Sc. A. 20 (1896) (Pt. 1) 56-. 

 Lame's equation. Brioschi, F. C. B. 85 (1877) 



1160- ; 86 (1878) 313-. 

 -- . Hermite, C. [1877] A. Mt. 9 (1878-79) 



-- . Lindemann, C. L. F. B. A. Bp. (1883) 



Lemniscate functions, expansion coefficients. 



Hurwitz, A. Gott. Nr. (1897) 273-; Mth. 



A. 51 (1899) 196-. 

 Linear differential equations. Stenberg, E. A. 



Helsingf. Acta 16 (1888) 333-. 



with doubly periodic coefficients. 

 Malmborg, M. Ups. irsk. (1897) (Mt. Nt.) 

 31pp. 



homogeneous differential equations, with 

 doubly periodic coefficients. Stenberg, E. A. 

 Helsingf. Acta 16 (1888) 493-, 555-; 19 

 (1893) No. 11, 7 pp. 



Periodic equation. Rodrigues, J. M. G. Teix. 

 J. Sc. 6 (1885) 191-. 



function of one variable with more than two 

 periods impossible, theorem of Jacobi. Caso- 

 rati, F. Mil. I. Lomb. Ed. 15 (1882) 623-. 



functions. Laurent, H. N. A. Mth. 6 

 (1867) 267-. 



, generalisation. Picard, E. C. B. 89 



' (1879) 140-. 



of 2nd kind. Rausenberger, 0. Mth. A. 



20 (1882) 550-. 

 , theory, fundamental theorem. Prings- 



heim, A. [1900] Munch. Ak. Sb. 30 (1901) 



541-. 

 , uniform, of not more than two periods. 



Gade, K. (xn) Ts. Mth. 5 (1881) 181-. 

 Problem of Abel, complement to. Bougaief, . 



C. B. 113 (1891) 1025-. 



proposed by Hermite, solution. Le 

 Vavasseur, . Toul. Fac. Sc. A. 8 (1894) 



G, 3 pp. 



" illipti 



Par. 



. Greenhill, A. G. [1888] L. Mth. S. 



P. 20 (1889) 213-. 

 . Floquet, G. C. B. 121 (1895) 805-, 



Pseudo-elliptic integrals. Goursat, E. 

 S. Mth. Bll. 15 (1887) 106-. 



. Halphen, G. H. C. B. 106 (1888) 



1263-. 



. Burnside,W. Mess. Mth. 22 (1893) 83-. 



, Abel's. Dolbnia, I. P. Kazan S. 



Nt. (Ps.-Mth.) P. 8 (1890) 252-; Liouv. J. 

 Mth. 6 (1890) 293-. 



depending on cube root of trinomial. 



- ,, . Dolbnia, J. Bll. Sc. Mth. 17 (1893) 125-. 



- _. Markoff, A. Mth. A. 47 (1896) 598- J_ _ radicals of 4th an v d 6th ; de g r ees. 



"rV-r 1 ? ^ a / 1 1 n ^ Hermite, C. [1879] Crelle Dolbnia, J. Bll. Sc. Mth. 17 (1893) 288-. 



J. Mth. 89 (1880) 9-. and their dynamica i applications. 



, new ivppliCcition. (ji/luCH, J A., Jd. ~ r*<nn*ii**ii A n MQQUI T M>V> Q T> o^ 

 C. B. 93 (1881) 537- S) 195- 



"o^'iao^oa 11 ' Craw f rd ' L ' Q J " Mth ' -, evaluation. Gilnther, S. Par. S. 



t (loyoj yo . 

 , , factors. 



29 (1898) 196-. 



, special case. Stenberg, E. A. 

 Mth. 10 (1887) 339-. 



, . Jamet, V. C. B. Ill (1890) 



638-. 



, theorems. Brioschi, F. C. B. 92 

 (1881) 325-. 



Lame-Hermite differential equation. Brioschi, 

 F. St Pet. Ac. Sc. Bll. 35 (1894) 449-. 



Crawford, L. QJ. Mth. 

 Acta 



Legendre's "Fonctions elliptiques," revision of 



chaps, xxiv and xxvi. Greenhill, A. G. QJ. 



Mth. 19 (1883) 225-. 

 Lemniscate function, representation, geometric. 



Krimphoff, W. Crelle J. Mth. 110 (1892) 



73-. 

 sn u, multiplication. Schwering, K. 



Crelle J. Mth. 107 (1891) 196-. 



Mth. Bll. 10 (1882) 88-. 

 ^-formula leading to expression for E. 

 Cayley, A. Mess. Mth. 6 (1877) 63-. 



for sine-amplitude, method of obtaining. 

 Glaisher, J. W. L. [1879] L. Mth. S. P. 

 11 (1879-80) 45-. 



g-series. Heine, H. E. Crelle J. 32 (1846) 



210- ; 34 (1847) 285-. 

 . Catalan, E. Par. S. Mth. Bll. 19 (1891) 



145-. 

 , formula due to Jacobi. Catalan, E. C. 



Liege S. Sc. Mm. 15 (1888) No. 1, 32-. 

 , formulae. Catalan, E. C. Liege S. Sc. 



Mm. 15 (1888) No. 1, 197-, 241-. 

 , relation of Kronecker's. Igel, B. Mh. 



Mth. Ps. 8 (1897) 354-. 



for v/2K and 2Glir, coefficients. Glaisher, 



Ith. 



J. W. L. QJ. Mth. 21 (1886) 60-. 



322 



