4420 Hypergeometric Functions, etc. Legendre's Functions 4420 



order, especially 1 + * 2 x + .... 

 Me, J. 1869 Mth. A.' 2 1870 427 



and Jacobi's polynomials. Appell, P. C. E. 



89 (1879) 31-. 

 3rd order, special case. Saalschiltz, L. Z. 



Mth. Ps. 36 (1891) 278-, 321-. 



higher 



Thomae, J. [1869] Mth. A. 2 (1870) 427- 



, relations between. Thomae, J. Leip. 



Mth. Ps. B. 43 (1891) 459-. 



orders. Mellin, H. Helsingf. Acta 23 

 (1897) No. 7, 10pp. 



with 5 parameters, differential equation. 



Markov, A. A. St P6t. Ac. Sc. Mm. 5 



(1897) No. 5, 23 pp.; Fschr. Mth. (1897) 



288-. 

 product of two, theorems. Orr, W. McF. 



[1898] Camb. Ph. S. T. 17 (1899) 1-. 

 representation by definite integral. Schafheit- 



lin, P. Mth. A. 30 (1887) 157-. 

 roots. Gegenbauer, L. Mh. Mth. Ps. 2 (1891) 



125-. 

 . Porter, M. B. N. Y. Am. Mth. S. Bll. 3 



(1897) 274-; 6 (1900) 280-. 

 with two singular points, more general, diffe- 

 rential equation. Pochhammer, L. Crelle 



J. Mth. 102 (1888) 76-. 

 special case, identities. Blissard, J. [1864] 



QJ. Mth. 7 (1866) 155-, 223-. 

 theory. Gegenbauer, L. Wien Ak. Sb. 100 



(1891) (^6. 2a) 225-. 

 transformation into continued fraction. Muir, 



T. L. Mth. S. P. 7 (1875-76) 112-. 

 2 variables. Appell, P. C. B. 90 (1880) 



977-. 

 Picard, E. C. B. 104 (1887) 896-. 



, contiguous functions relative to. 

 Levavasseur, . C. B. 115 (1892) 1255-. 



, and linear partial differential equations. 



AppcU, P. C. B. 90 (1880) 296-, 731-. 



, uniform functions arising from. 

 Goursat, E. C. B. 104 (1887) 893-. 



zeros. Hurwitz, A. Gott. Nr. (1890) 557-. 



. Klein, F. Mth. A. 37 (1890) 573-. 



F (a, /3, 7, x), cases where it is algebraic 



function of its fourth element. Schwarz, 



H. A. [1871-72] Sch. Gs. Vh. 54 (1871) 



74-; Crelle J. 75 (1873) 292-. 

 F 1 (a, /3, p, 7; x, y), partial differential 



equations satisfied by. Le Vavasseur, R. 



Toul. Fac. Sc. A. 7 (1893) F, 205 pp. 

 for x\ Jackson, (Rev.) F. H. Edinb. Mth. 



S. P. 15 (1897) 90-. 



Hypergeometric theorems 



Q=F(-2m-l, -n, -2n, 2) 



(-2m, -n, -2n,2). 



Bretschneider, C. A. Grunert Arch. 13 

 (1849) 223. 



transcendentals, representation by uniform 

 functions. Papperitz, E. Mth. A. 34 (1889) 



Hyperspherical functions, and development of 

 any function in series of. Letnikov, A. V. 

 Bee. Mth. (Moscou) 12 (1885) 205-. 



Icosahedra, regular. Klein, C. F. Erlang. 

 Ps. Md. S. Sb. 9 (1877) 16-, 70-, 179- ; 

 Mth. A. 12 (1877) 503-. 



Integral I P dx and allied forms between arbi- 

 trary limits. Hargreaves, R. [1897] L. 

 Mth. S. P. 29 (1898) 115-. 



Kleiber's functions K t and G 4 . Glaisher, J. 

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



Rummer's equation. Goursat, $. Helsingf. 

 Acta 15 (1888) 45-. 



, integration. Lindeldf, E. Helsingf. 

 Acta 19 (1893) No. 1, 31 pp. 



Lame's, Laplace's and Bessel's functions, con- 

 nexion between. Raentzschel, E. Z. Mth. 

 Ps. 31 (1886) 25-. 



Laplace's and Bessel's functions, relation 

 between. Rayleigh, J. W. Strutt (Lord). 

 L. Mth. S. P. 9 (1877-78) 61-. 



coefficients, expansion of integral functions 

 in series, of. Cayley, A. Camb. and Dubl. 

 Mth. J. 3 (1848) 120-. 



, F (/j. w) in series of. Goodwin, H. 



Camb. Mth. J. 2 (1841) 223-. 



6g coefficients. Radau, R. Bll. As. 13 

 (1896) 5-. 



equation. Tychsen, C. (xn) Ts. Mth. 6 

 (1876) 165-. 



functions, equation, solution. Graves, G. 

 Ir. Ac. P. 6 (1853-54 162-, 186-, 221-. 



, , . Hamilton, (Sir) W. R. Ir. Ac. 



P. 6 (1853-54) 181-. 

 Legendre's coefficients. Todhunter, I. B. S. 



P. 27 (1878) 381-. 

 . Webb, R. R. [1879] Mess. Mth. 9 



(1880) 125-. 

 and complete elliptic integral, connexion 



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



(1884) 161-. 

 , product of any two as series of Legendre's 



coefficients. Adams, J. C. [1877] E. S. P. 



27 (1878) 63-. 



, theorems. Zanotti Bianco, 0. Tor. 

 Ac. Sc. At. 22 (1886-87) 225-; 23 (1887-88) 

 5. 



, value for n great. Sharpe, H. J. QJ. 



Mth. 24 (1890) 383-. 



equation, solution in a particular case. 

 Forsyth, A. R. Mess. Mth. 16 (1887) 168-. 



LEGENDBE'S FUNCTIONS. 



RoucM, E. C. B. 47 (1858) 917-. 

 Laurent, H. Liouv. J. Mth. 1 (1875) 373-. 

 (Laurent.) Heine, H. E. Liouv. J. Mth. 2 



(1876) 155-. 

 Catalan, E. C. As. Fr. C. B. 5 (1876) 68-; 



Brux. Mm. Cour. 8, 31 (1881) (No. 3) 64 pp. ; 



Brux. Ac. Sc. Mm. 43 (1882) (No. 9) 10 pp.; 



44 (1882) (No. 1) 103 pp. ; 46 (1886) (No. 5) 



28 pp.; 47 (1889) (No. 1) 12 pp., (No. 4) 

 12 pp., (No. 5) 24 pp. 



Laguerre, E. C. E. 91 (1880) 849-. 



Deruyts, J. Liege S. Sc. Mm. 11 (1885) No. 8, 



22 pp. 

 analogues to. Didon, F. Par. EC. Norm. 



A. 5 (1868) 229-. 



346 



