4420 



Legendrian and Hypergeometric Functions 



4420 



analogues to. Deruyts, J. Liege S. Sc. Mm. 



14 (1888) No. 2, 15 pp. 



calculation for high values of n. Callandreau, 



O. Bll. Sc. Mth. 15 (1891) 121-. 

 expansion of function in series of functions 



similar to. Andreev, K. A. St Pet. Ac. Sc. 



Mm. (Rs.) 51 (1885) 1-; F.schr. Mth. (1885) 



500. 

 functions connected with, and derivable from 



complete elliptic integrals. Kleiber, J. Mess. 



Mth. 22 (1893) 1-. 



similar to. CebySev, P. [1869] St Pet. 

 Ac. Sc. Mm. (Es.) 16 (*1870) 131-. 



. Posse, K. A. Kharkov Mth. S. 



Com. (1885) 155- ; Fschr. Mth. (1886) 430. 

 generalisation. Hansted, B. [1881] G. Teix. 



J. Sc. 4 (1883) 53-. 



arising from development of 



.am 

 [l-2euc + a 2 ] 2 



Escary, . Liouv. J. Mth. 5 (1879) 47-. 

 for n infinite. Giuliani, G. G. Mt. 22 (1884) 



236-. 

 and Lamp's functions. Schmit, N. C. Liege 



Mm. S. Sc. 13 (1858) 289-. 

 new form for. Catalan, E. Par. S. Mth. Bll. 



16 (1888) 128-. 

 polynomials analogous to. Didon, F. Par. 



EC. Norm. A. 7 (1870) 247-. 

 properties, general. Biervliet, A. van. (xn) 



Brux. S. Sc. A. 7 (1883) (Ft. 1) 68-, (Pt. 2) 



402-. 

 , new. Catalan, E. C. Lie"ge S. Sc. Mm. 



15 (1888) No. 1, 122-. 



of series involving. Plarr, G. C. E. 44 

 (1857) 984-. 



transformation into definite integral. Silva, 

 J. A. Martins da. G. Teix. J. Sc. 3 (1881) 



Legendre's polynomials. 



Hermits, C. G. Teix. J. Sc. 6 (1885) 81-; 



Palermo Cir. Mt. Ed. 4 (1890) 146-. 

 Stieltjes, T. J. Toul. Fac. Sc. A. 4 (1890) G, 17pp. 

 Hermite, C. Crelle J. Mth. 107 (1891) 80-. 

 Morera, G. Palermo Cir. Mt.Ed. 11 (1897) 176-. 

 asymptotic expression of. Lerch, M. [1891] 



Prag Ceske Ak. Fr. Jos. Ez. (Tfida 2) 1 



(1892) Art. 8, 27-. 

 class of associated polynomials analogous to. 



Deruyts, J. Liege S. Sc. Mm. 14 (1888) 



No. 3, 14 pp. 

 generalisation. Clariana Eicart, L. [1892] 



Barcel. Ac. Bl. 1 (1892-1900) 73-. 



of formula. Gegenbauer, L. Palermo Cir. 

 Mt. Ed. 12 (1898) 21-. 



and Hermite' s and Polignac's. Catalan, E. C. 



Brux. Ac. Mm. 49 (1890-93) (No. 4) 48 pp. 

 limit. Gomes Teixeira, F. Prag Sb. (1886) 



(Mth.-Nt.) 19-. 



theorem. Stieltjes, . C. E. 100 (1885) 439-. 

 theory. Hilbert, D. Acta Mth. 18 (1894) 155-. 



Legendrian coefficient, formulas for rth integral. 

 Glaisher, J. W. L. [1882] Mess. Mth. 12 

 (1883) 120-. 



Polygons, area, theorem. Tardy, P. Tortolini 



A. 3 (1852) 116-. 



Poly-harmonic functions, i.e. solutions of 

 / d* d 2 \ 

 V^ 2 + d?) ' 



in simply connected plane space. Almansi, E. 



Palermo Cir. Mt. Ed. 13 (1899) 225-. 

 Polynomials A^ n of 2 variables analogous to 



Jacobi's. Appell, P. [1880] Arch. Mth. 



Ps. 66 (1881) 238-. 



Pm,n f Didon, generating function. Orlow, 

 G. A. N. A. Mth. 20 (1881) 481-. 



Eeduction of a certain integral. Zinin, N. N. 



Eec. Mth. (Moscou) 14 (1890) 549-. 

 Eiemann's P-function, mathematical repre- 



sentation. Radicke, A. Epm. Mth. 1 (1877) 



50-. 



functions of 2nd order with four branch- 

 points. Heun, K. Mth. A. 33 (1889) 161-. 



Eodrigues's theorem (formula for 



/ d \i 



(E) 



= (*-!) 



Hudson, W. H. H. [1877] Mess. Mth. 7 



(1878) 117. 

 , demonstration. Hogg, R. W. Mess. 



Mth. 14 (1885) 20. 



Series of Gauss. Tano, F. G. Mt. 9 (1871) 60-. 

 , generalised form, cases. Glaisher, J. W. L. 



L. Mth. S. P. 9 (1877-78) 197-. 



of Heine. Tano, F. G. Mt. 9 (1871) 60-. 



, elements, threefold symmetry in. 

 Rogers, L. J. L. Mth. S. P. 24 (1893) 171-. 



, higher. Thomae, J. A. Mt. 4 



(1870-71) 105-. 



, transformation. Rogers, L. J. 

 Mess. Mth. 23 (1894) 28-. 



(x-l) x(x-T)(x-2) 

 (z-l)(z-2) 

 x(x-l)(x-2)(x-3) 

 z (z - 1) (z - 2) (z - 3) 



summation. Grunert, J. A. Crelle J. 2 

 (1827) 358-. 



-+..., summation. 



Schlomilch, 0. Grunert Arch. 3 (1843) 442-. 



F(v, x, k, a) with relation to Euler's 

 formula (also expressed as sum of definite 

 integrals). Lipschitz,R. Crelle J. 54 (1857) 

 313-. 



2 n A n X n . Ascoli, G. A. Mt. 7 (1876) 258-. 



Solution of 



Steinthal, A. E. QJ. Mth. 18 (1882) 330-. 



Spherical harmonics. 



Betti, E. [1867] A. Mt. (1867-68) 81-. 

 Sylvester, J. J. Ph. Mg. 2 (1876) 291-, 400. 

 Beltrami, E. Mil. I. Lomb. Ed. 20 (1887) 469-. 



347 



