4040 



Elliptic and Single Theta Functions 



extension. Winckler, A. Wien SB. 44 (1861) 



(Ab. 2) 477-. 

 and inversion problem. Brill, A. Mth. A. 17 



(1880) 87-. 

 of Jacobi and of Weierstrass. Study, E. Am. 



J. Mth. 16 (1894) 156-. 

 proof. Griffiths, J. L. Mth. S. P. 13 (1881- 



82) 177-. 

 for theta functions. Caspary, F. C. B. 104 



(1887) 1255-. 



transcendental functions. Pokrovskij, P. M. 

 Eec. Mth. (Moscou) 18 (1896) 121- ; Fschr. 

 Mth. (1896) 360. ' 



, integration of differential equations 



leading to. Steen, A. Kjob. Skr. 8 (1870) 

 1-; Resume, 15-. 



Hu) and for cotangent. Schottky, F. Crelle 

 J. Mth. 110 (1892) 324-. 



g? (u), elementary deduction. Anissimow, . 

 [1893] Fschr. Mth. (1893-94) 767. 



. Stdckel,P. Mth. A. 47 (1896) 604. 



Arithmetico-geometric mean. Borchardt, C.W. 



[1858] Crelle J. 58 (1861) 127-. 

 . Frisby, E. Des Moines Anal. 6 



(1879) 10-. 

 . Lohnstein, T. Z. Mth. Ps. 33 (1888) 



129-, 318. 

 of 4 elements (Borchardt). Schering, 



K. Crelle J. Mth. 85 (1878) 115-. 



Class dxlU x ^+ ... where U x =(a,b,c,d,e)(x, 1). 

 Russell, R. QJ. Mth. 20 (1885) 179-. 



dxlU x *+... where U x =(a, b, c, d, e) (x, - I) 4 . 

 Russell, R. QJ. Mth. 20 (1885) 265-. 



Closed polygons in- and circum-scribed to 



conies. Oekinghaus, E. Arch. Mth. Ps. 6 



(1888) 186-. 

 Complete elliptic integrals. Smith, H. J. S. 



Km. B. Ac. Line. T. 1 (1877) 42-. 



, functions derivable from, and con- 

 nected with Legendre's functions. Kleibner, 



J. Mess. Mth. 22 (1893) 1-. 

 , 1st kind, formula relating to. Besso, 



D. Bm. B. Ac. Line. Ed. 4 (1895) (Sem. 1) 



229-. 

 , , and Legendre's coefficients, 



connection. Stuart, G. H. Mess. Mth. 13 



(1884) 161-. 

 , , quotient, extension of theorem 



of Biemann. Torelli, G. Nap. Bd. 29 



(1890) 238-. 



, and 2nd kinds, approxima- 

 tions. Lodge, A. Mess. Mth. 28 (1899) 

 17-. 



, , continued fraction for 

 ratio. Baraniecki, M. A. Par. T. Nauk S~c. 

 Pam. 7 (*1875) Art. 5, 8 pp. 



, , representation in 

 simple form. Radicke, A. Z. Mth. Ps. 21 

 (1876) 442-. 



, 2nd kind, expression by sines of 



multiples of modular angle. Glaisher, 

 J. W. L. Ph. Mg. 19 (1885) 504-. 



, , reduction to complete elliptic 



integrals of 1st kind for same modulus. 

 Meissel, E. Arch. Mth. Ps. 56 (1874) 337-. 



4040 



Conjugate functions of Cartesians and other 

 quartics. Greenhill, A. G. [1881] Camb. 

 Ph. S. P. 4 (1883) 77-. 



Definite theta-function integrals, cases. Rogers, 

 L. J. [1894] L. Mth. S. P. 26 (1895) 

 145-. 



Differential equation in elliptic functions, geo- 

 metrical illustration of solution. Hart, H. 

 Mess. Mth. 4 (1875) 125-. 



, Euler's. Halphen, G. H. Palermo Cir. 



Mt. Bd. 2 (1888) 40-. 



, 2nd order, for & (u). Mittag-Leffler, G. 



C. K. 117 (18931 92-. 



, remarkable, integration. Picart, A. 

 C. B. 66 (1868) 1192-. 



satisfied by I2q + 2q*2q 9 + .... Jacobi, 



C. G. J. Liouv. J. Mth. 14 (1849) 181-. 



equations, class. Catalan, . As. Fr. C. B. 

 (1886) (Pt. 1) 85. 



and elliptic series. Liouville, J. Liouv. 



J. Mth. 14 (1849| 225-. 



expression, reduction. Manning, H. P. 

 Am. J. Mth. 13 (1891) 185-. 



dt-\lt -a.t-p.t-y.t-8, reduction 



to standard form. Griffiths, J. L. Mth. S. 

 P. 14 (1882-83) 196-. 



Doubly periodic functions. 



Liouville, J. Crelle J. Mth. 88 (1880) 277-. 

 arising from x 3 + y 3 -3axy = l. Dixon, A. (7. 



QJ. Mth. 24 (1890) 167-. 

 considered as limits of algebraic functions. 



Biehler, C. [1879] Crelle J. Mth. 88 (1880) 



185-. 

 with essential singular points. Picard, E. C. 



B. 89 (1879) 852-. 

 expansion in Fourier's series. Charlier, C. V. L. 



Stockh. Ak. Hndl. Bh. 12 (Afd. 1) (1887) 



No. 9, 24 pp.; Fschr. Mth. (1887) 448. 

 trigonometric series. Krause, M. D. 



Nf. Tbl. (1889) 188-. 

 expression by definite integrals and arithmetical 



invariants. Poincare, H. As. Fr. C. B. 



(1881) 109-. 

 Fourier's expansion for, new method. Mohr- 



mann, G. Arch. Mth. Ps. 12 (1894) 1-. 

 Hermite's memoir. Cauchy, A. L. C. B. 32 



(1851) 442-. 

 of 2nd kind. Mittag-Leffler, G. C. B. 90 



(1880) 177-. 

 . Gegenbauer, L. [1882] Wien Ak. 



Sb. 86 (1883) (Ab. 2) 969-. 

 . Goursat, E. C. B. 98 (1884) 



35-. 

 . Teixeira, J. P. G. Teix. J. Sc. 



9 (1889) 103- ; Fschr. Mth. (1889) 471. 

 , application. Hermite, . Par. EC. 



Norm. A. 2 (1885) 303-. 



, differential equations satisfied by. 

 Krause, M. Leip. Mth. Ps. B. 42 (1890) 

 55-, 268-, 430- ; 43 (1891) 32-, 289-, 597-. 



and 3rd kinds. Krause, M. Leip. Mth. 



Ps. B. 41 (1889) 347-. 



3rd kind. Appell, P. Par. EC. Norm. A. 

 1 (1884) 135- ; 2 (1885) 9-; 3 (1886) 9-; 

 C. B. 101 (1885) 1478-. 



312 



