4420 



Hypergeometric Functions 



4420 



analogues to. Goursat, E. Par. EC. Norm. A. 



3 (1886) 107- . 

 arising from Gauss's equation. Halphen, G.H. 



G. E. 92 (1881) 856-. 

 and Bessel's functions, roots. Porter, M. B. 



Am. J. Mth. 20 (1898) 193-. 

 with branchings (2, 3, 7), (2, 4, 7), arithmetical 



theory. Fricke, E. Mth. A. 41 (1893) 443-. 

 case. Markov, A. A. [1892] St Pet. Ac. Sc. 



Mm. 41 (1893) No. 2, 37 pp. 

 last element of which has special value. Hey- 

 mann, W. Z. Mth. Ps. 44 (1899) 280-. 

 expression as definite integrals. Mellin, H. 



Helsingf. Acta 20 (1895) No. 1, 39 pp.; 



Fschr. Mth. (1895) 481. 

 extension of Eiemann's problem to functions of 



2 variables. Picard, E. [1880] Par. EC. 



Norm. A. 10 (1881) 305-. 

 . Goursat, E. C. E. 



95 (1882) 903-, 1044- ; 96 (1883) 185-. 

 of form 



pp'p" p.p + l.p'p' + l p".p" + l 

 + l.q'q" + 1.2.q'.q' + l q".q" + l' 



Thomae, C. J. Crelle J. Mth. 87 (1879) 26-. 

 and gamma functions, application of Cauchy's 



theorem. Mellin, H. Helsingf. Acta 21 



(1896) No. 1, 115pp. 

 generalisation. Pincherle, S. Em. E. Ac. 



Line. Ed. 4 (1888) (Sem. 1) 694-, 792-. 

 history. Papperitz, E. Dresden Isis Sb. 



(1889) (Ab.) 61-. 

 2nd kind and higher order. Beaupain, J. 



Brux. Mm. Cour. 4, 54 (1896) No. 1, 46 pp., 



No. 8, 46 pp. 

 higher order. Goursat, E. Par. EC. Norm. 



A. 12 (1883) 261-, 395-. 

 . LUnikov, A. V. Eec. Mth. (Moscou) 



14 (1890) 216- ; Fschr. Mth. (1890) 443. 

 . Beaupain, J. Brux. Mm. Cour. 4, 56 



(1897-98) No. 2, 52 pp. 

 nth order. Pochhammer, L. [1869] Crelle J. 



71 (1870) 316-. 



. Fuchs, L. Crelle J. 72 (1870) 255-. 



simultaneous linear differential equations in- 

 tegrable by. Heymann, W. Z. Mth. Ps. 32 



(1887) 176-. 

 with singularity. Eitter, E. Mth. A. 48 (1897) 



theorem, fundamental. Baraniecki, M. A. 

 Par. T. Nauk Sc. Pam. 8 (*1876) Art. 2, 

 19 pp. ; Bll. Sc. Mth. As. 1 (*1877) (Pt. 2) 



2 variables. Goursat, E. C. E. 95 (1882) 717-. 



. Appell, P. Liouv. J. Mth. 10 (1884) 407-. 



, formulas. Appell, P. Liouv. J. Mth. 



8 (1882) 173-. 

 several variables. Lauricella, G. Palermo 



Cir. Mt. Ed. 7 (1893) 111-. 



Hypergeometric series. 



Hypergeometric integral, general, fundamental 

 values. Eadicke, A. Z. Mth. Ps. 22 (1877) 87-. 



integrals, nth order. Pochhammer, L. 

 [1870] Crelle J. 73 (1871) 135-. 



quantities, calculation. Multedo, . Ge- 

 nova Mm. I. Ligure 1 (1806) 1-; Geneva 

 Mm. Ac. 2 (1809) 230-. 



Gauss, C. F. Gott. Cm. 2 (1811-13) 46 pp. 

 Rummer, E. E. Crelle J. 15 (1836) 39-, 127-. 

 Cayley, A. Ph. Mg. 16 (1858) 356-. 

 Dronke, A. Schlomilch Z. 8 (1863) 401-. 

 Schlrifli, L. [1870] Mth. A. 3 (1871) 286-. 

 Gegenbauer, L. Arch. Mth. Ps. 55 (1873) 



284-. 

 Meissel, E. [1874] Arch. Mth. Ps. 57 (1875) 



Markoff, A. C. E. 114 (1892) 54-; Mth. A. 

 40 (1892) 313-. 



Graf, I. H. G. Mt. 36 (1898) 233-. 



case. Cayley, A. QJ. Mth. 16 (1879) 268-. 



class of equations of 6th order soluble by. 

 Besso, D. [1882] Em. E. Ac. Line. Mm. 14 

 (1883) 30-. 



in connexion with observation polygons. Pear- 

 son, K. Ph. Mg. 47 (1899) 236-. 



definite integrals connected with. Eajewski, J. 

 Krk. Ak. (Mt.-Prz.) Ez. 20 (1890) 272-; 

 Crc. Ac. Sc. Bll. (1890) 61-. 



and definite integrals, theorem. Catalan, E. C. 

 Liege S. Sc. Mm. 15 (1888) No. 1, 46-. 



definite integrals satisfying differential equa- 

 tion. Torelli, G. Em. S. It. Mm. 7 (1890) 

 No. 4, 18 pp. 



differential and difference equations integrable 

 by. Heymann, W. Crelle J. Mth. 122 

 (1900) 164-. 



equation. Jacobi, C. G. J. Crelle J. 56 

 (1859) 149-. 



. Spitzer, S. Crelle J. 57 (1860) 78-. 



(Spitzer). Borchardt, C. W. (vi Adds.) 



Crelle J. 57 (1860) 81. 

 . Markov, A. A. Kharkov Mth. S. Com. 



(1886) 51-, 95-; Mth. A. 28 (1887) 586-; 29 



(1887) 247-. 



. Pochhammer, L. Mth. A. 38 (1891) 



586-. 

 , 2nd solution. Johnson, W. W. Mess. 



Mth. 17 (1888) 35-. 



equations integrable by. Heymann, W. Z. 

 Mth. Ps. 29 (1884) 144-. 



satisfied by. Pochhammer, L. Mth. A. 



33 (1889) 353-. 

 divergent (or semiconvergent). Orr, W. McF. 



[1898] Camb. Ph. S. T. 17 (1899) 171-, 



283-. 

 elementary treatment. Thomae, C. J. Z. 



Mth. Ps. 26 (1881) 314- ; 27 (1882) 41-. 

 extension of theorem. Jackson, (Eev.) F. H. 



L. Mth. S. P. 28 (1897) 475-. 

 finite, discriminant. Hilbert, D. Crelle J. 



Mth. 103 (1888) 337-. 

 form of square. Clausen, T. Crelle J. 3 



(1828) 89-. 

 more general integral representation. Schaf- 



heitlin, P. Crelle J. Mth. 103 (1888) 89-. 

 Heine's, analogy of series. Lerch, M. 



[1893] Prag Ceske Ak. Fr. Jos. Ez. (Trida 2) 



3 (1894) Art. 5, 10 pp.; Fschr. Mth. (1893-94) 



794. 

 integral function equal to product of two. 



Markov, A. A. Kharkov Mth. S. Com. 3 



(1893) 252-; Fschr. Mth. (1892) 408-. 



345 



