4410 



Gamma Functions 



4410 



Lerch, M. Prag Cesk6 Ak. Fr. Jos. Ez. 



(TKda 2) 5 (1896) Art. 14, 37 pp. ; Fschr. 



Mth. (1896) 333. 

 analogues to. Alekseevskij, V. P. Kharkov 



Mth. S. Com. 1 (1889) 169- ; Fschr. Mth. 



(1890) 439-; Leip. Mth. Ps. B. 46 (1894) 



268-. 

 and analytical factorials. Hoppe, E. [1845] 



Crelle J. 40 (1850) 152-. 

 with arbitrary parameter. Bigler, . Crelle 



J. Mth. 102 (1888) 237-. 

 and beta functions, relations between. Spitzer, 



S. D. Nf. Tbl. (*1876) (Beil.) 63. 



, series connected with. Lerch, M. 

 G. Teix. J. Sc. 10 (1891) 103-. 



of a complex. Sharpe, H. J. Mess. Mth. 



13 (1884) 111-. 

 deduced from S(ic + n)-*. Lerch, M. Prag 



Ceske Ak. Fr. Jos. Ez. (Tfida 2) 8 (1899) 



Art. 35, 9 pp. ; Fschr. Mth. (1899) 392. 

 and definite integrals. Matthiessen, L. Z. 



Mth. Ps. 12 (1867) 302-. 

 derivatives. Jeffery, H. M. [1862] QJ. Mth. 



6 (1863) 82-. 

 double. Barnes, E. W. [1900] Phil. Trans. 



(A) 196 (1901) 265-. 

 , genesis. Barnes, E. W. L. Mth. S. P. 31 



(1900) 358-. 

 evaluation of infinite factorials by. Weyr, E. 



Casopis 22 (1893) 161- ; Fschr. Mth. (1893- 



94) 750. 

 expansion embracing series of Stirling and 



Kummer. Landsberg, G. Brux. Mm. Cour. 



8, 55 (1896-98) No. 4, 28 pp. 



and integrals depending on it. Gilbert, L. P. 

 [1873] Brux. Ac. Mm. 41 (Pt. 1) (1875) (No. 3) 

 60 pp. 



expression of definite integrals by. Graf, J. H. 



Bern Mt. (1884) (Heft 2, Ab.) 46-. 

 expressions in terms of complete elliptic 



integrals. Glaislier, J. W. L. Mess. Mth. 



24 (1895) 27-. 

 and factorials. Ohm, M. Crelle J. 36 (1848) 



277-. 



figurate numbers, binomial coefficients in 

 relation to. Matthiessen, . D. Nf. Tbl. 

 (*1868) 128-. 



formula. Lerch, M. Mh. Mth. Ps. 8 (1897) 

 187-. 



_ J" <(> (x + a) a*' 1 do = (- If I* <t> (x)dx*. 



Liouville, J. Crelle J. 12 (1834) 273-. 

 formulae. Genocchi, A. Brux. Ac. Bll. 21 



(1854) 84-. 

 . Lindhagen, A. Stockh. Ofv. 40 (1883) 



No. 2, 27-. 

 function related to. Schlomilch, O. X. Z. 



Mth. Ps. 25 (1880) 335-. 

 Gauss's expression for. Arndt, F. Grunert 



Arch. 10 (1847) 250-. 

 T(M). Zehfuss, G. Grunert Arch. 



30 (1858) 441. 

 generalisation of equation 



r (1 + x) r (1 - x) = Trx/sin vx. 

 Mellin, H. Acta Mth. 3 (1883) 102-. 



and hypergeometric functions, application of 



Cauchy's theorem. Mellin, H. Helsingf. 



Acta 21 (1896) No. 1, 115 pp. 

 incomplete. Hocevar, F. Z. Mth. Ps. 21 



(1876) 449-. 

 , continued fraction for. Schlomilch, O. 



Z. Mth. Ps. 16 (1871) 261-. 

 and infinite products. Bauer, G. Crelle J. 



57 (1860) 256-. 

 . Mellin, H. Acta Mth. 3 (1883) 



322-; Helsingf. Ofv. 26 (1884) 170-. 

 integrals expressible by. Schlomilch, 0. Z. 



Mth. Ps. 9 (1864) 256-. 

 2nd kind. Serret, J. A. Liouv. J. Mth. 



7 (1842) 114-. 



. Schlomilch, O. Grunert Arch. 4 

 (1844) 167-. 



. Liouville, J. Liouv. J. Mth. 11 

 (1846) 464-. 



, general properties. Schlomilch, O. 

 Grunert Arch. 6 (1845) 213-. 



, negative minima. Glaisher, J. W. L. 



B. A. Ep. 43 (1873) (Sect.) 13. 



, theorem. Liouville, J. Liouv. J. Mth. 

 20 (1855) 157-. 



, , Legendre's. Schlomilch, 0. 

 Grunert Arch. 7 (1846) 348-. 



Legendre's. Liouville, J. Liouv. J. Mth. 



17 (1852) 448-. 

 , Gauss's formula, demonstration. Liouville, 



J. C. R. 42 (1856) 501-. 

 logarithm. Binet, J. P. M. C. E. 9 (1839) 



156-. 

 . Hermite, C. Am. J. Mth. 17 (1895) 



111-, 

 of negative quantity. Newman, F. W. Camb. 



and Dubl. Mth. J. 3 (1848) 57-. 

 new notation in connexion with. Lindner, P. 



Arch. Mth. Ps. 70 (1884) 96-, vrn. 

 with a power as argument, property. Eggen- 



berger, J. Bern Mt. (1895) 8-. 

 property of satisfying no algebraic differential 



equation. Holder, O. Mth. A. 28 (1887) 1-. 

 properties. Blissard, J. QJ. Mth. 9 (1868) 



280-. 

 quotient of two. Schlomilch, 0. X. Z. Mth. 



Ps. 25 (1880) 351-. 

 reciprocal value. Schlomilch, O. X. Z. Mth. 



Ps. 25 (1880) 103-. 

 series for. Schlomilch, G. Schlomilch Z. 



4 (1859) 431-. 

 and Stirling's series. Genocchi, A. Em. S. 



It. Mm. 6 (1887) No. 2, 24 pp. 

 theorem, Gauss's, demonstration. Sonine, N. J. 



Par. S. Mth. Bll. 9 (1881) 162-. 

 theory. Kummer, E. E. Crelle J. 35 (1847) 1-. 

 . Prym, F. E. Crelle J. Mth. 82 (1877) 



165-. 



. Mellin, H. Acta Mth. 8 (1886) 37-. 

 . Pringsheim, A. Mth. A. 31 (1888) 455-. 

 . Barnes, E. W. Mess. Mth. 29 (1900) 64-. 

 , definite integrals from. Lerch, M. Prag 



Ceske Ak. Fr. Jos. Ez. (TKda 2) 8 (1899) 



Art. 37, 5 pp.; Fschr. Mth. (1899) 391. 

 , elementary exposition. Jensen, J. L. W. V. 



N. Ts. Mth. 2 (B) (1891) 33-, 57-, 83-; 



Fschr. Mth. (1891) 445-. 



341 



