4410 



Eulerian and Gamma Functions 



4420 



theory, formulae, generalisation. Berger, A, 



Stockh. Ofv. 38 (1881) No. 9, 13-. 

 , Gauss's equation. Lerch, M. Prace 



Mt.-Fiz. 10 (1899-1900) 1-, 269-; Fschr. 



Mth. (1899) 390. 

 , point in. Lerch, M. Prag Sb. (1893) 



(Mth.-Nt.) No. 26, 8 pp. 

 transcendental function connected with, and 



application to integration. Kinkelin, H. 



Crelle J. 57 (1860) 122-. 

 functions related to. Mellin, H. Helsingf. 



Acta 14 (1885) 353-; 15 (1888) 1-; Fschr. 



Mth. (1886) 441-. 

 transformations connected with. Catalan, E. C. 



Liege S. Sc. Mm. 15 (1888) No. 1, 64-, 103-. 



Gamma integral, property. Bjorling, E. G. 



Stockh. Ofv. 13 (1856) 181-. 

 Generalisation of Eulerian functions. Pin- 



cherle, S. C. B. 106 (1888) 265-. 

 Interpolation of some products. Steklov, V. A. 



Kharkov Mth. S. Com. 1 (1889) 239-; Fschr. 



Mth. (1890) 439. 

 Malmsten series. Lerch, M. Prag Ceske" Ak. 



Fr. Jos. Bz. (Trida 2) 3 (1894) Art. 28, 1-; 



Fschr. Mth. (1893-94) 484-. 

 . Hermite, C. Prag Ceske Ak. Fr. Jos. 



Bz. (Tftda 2) 3 (1894) Art. 28, 62-; Fschr. 



Mth. (1893-94) 484-. 

 Periodic functions. Scheibner, W. Leip. B. 



14 (1862) 64-. 

 Prym's and Hermite's functions. Genocchi, A. 



Brux. Ac. Bll. 4 (1882) 438-; 5 (1883) 421-. 



Bapidly converging series for 



T(w) 



Lerch, M. 



Prag Ceske Ak. Fr. Jos. E'z.' (Tfida 2) 8 



(1899) ^rt. 36, 9 pp. ; Fschr. Mth. (1899) 390-. 

 Eeduction of certain integrals to Eulerian 



functions. Beaupain, J. Brux. Mm. Cour. 



4, 51 (1889) No. 6, 40 pp. 

 Stirling's formula. Rouche, E. C. E. 110 



(1890) 513-. 

 , demonstration. Catalan, E. C. Liege 



S. Sc. Mm. 12 (1885) No. 2, 221-. 

 Theorem of Legendre, demonstration. Stern, 



M. A. [1866] Crelle J. 67 (1867) 114-. 

 Vandermonde, extension. Jackson, F. H. 



L. Mth. S. P. 26 (1895) 285-. 

 Theorems of Fermat. StudnMka, F. J. Casopis 



29 (1900) 257-; Fschr. Mth. (1900) 438. 



p-j rr, demonstration. Jacobi, C. G. J. Crelle 



J. 11 (1834) 307. 



Po;P- 1 rf:r(l-z). Plana, G. Crelle J. 17 

 (1837) 1-, 163-, 338-. 

 I xt>- l dx(l-x)i- 1 , p or q being rational. 



Binet, J. P. M. C. E. 16 (1843) 377-. 

 r(ra+l), approximation when n is large. Raabe, 



J. L. Crelle J. 25 (1843) 146-; 28 (1844) 10-. 

 F(a), theory, supplement. Gudermann, C. 



Crelle J. 29 (1845) 209-. 



r (x) r (x + ^\ = 2!-2V^ . T (2z) . Liouville, J. 

 Liouv. J. Mth. 20 (1855) 161-. 



(a;), fundamental equations. Kinkelin, H. 

 [1856] Bern Mt. (1857) 1-. 



-;r ^- Oltramare,G.Gen. 



I. Nt. Mm. 4 (1856) (pte. 2) 33-. 

 II (2) complex variable. Enneper, A. QJ. Mth. 



1 (1857) 393-. 

 log Tx, differentials. Clausen, T. Grunert 



Arch. 30 (1858) 166-. 



?. Tor. 



/ 1 + 2x fe cos + x* 



Mm. Ac. 18 (1859) 499-. 

 logr(l + a), approximation. Limbourg, H. 



Brux. Mm. Cour. 4, 30 (1861) 21 pp. 



2 =-r-r, calculation. Gasparis, A. de. Nap. 



Ed! 6 (1867) 276-. 



II (#), and imaginary triangles, etc. Grunert, 

 J. A. Arch. Mth. Ps. 51 (1870) 423-. 



logTx(dx). Bierens de Haan, D. Amst.Vs. 



Ak. 7 (1873)26-; Arch. Neerl. 8 (1873) 148-. 



?r(x), expansions. Gilbert, P. Brux. Ac. 



Bll. 36 (1873) 541-. 

 , . Genocchi, A. Brux. Ac. Bll. 36 (1873) 



546-. 

 . Genocchi, A. Arch. Mth. Ps. 61 (1877)366-. 



T ( ^ j , calculation. Kummell, C. H. Des 



Moines Anal. 4 (1877) 156-, 182-. 

 r(z), etc., applications. Appell, P. C. E. 86 

 (1878) 953-. 



J l log T (x + u) du. Stieltjes, T. J. (jun.) . N. 



Arch. Wisk. 4 (*1878) 100-. 

 P (x), maxima and minima. Bourguet, L. 



Tor. Ac. Sc. At. 16 (1881) 758-. 

 T(x)-P(x) = Q(x). Mellin, H. Acta Mth. 



2 (1883) 231-. 

 logr(a), expansion. Stieltjes, T. J. Liouv. 



J. Mth. 5 (1889) 425-. 

 log r (x) represented as a definite integral. 



Gomes Teixeira, F. Fschr. Mth. (1891) 450. 

 r(a). Poch1iammer,L. Mth. A. 41 (1893) 157-. 

 r(l + i), numerical value. Cayley, A. Mess. 



Mth. 23 (1894) 36-. 



0( 7 )-_ r e'^dt, table. Kampfe, B. Ph. 

 Virjo 



Stud. 9 (1894) 145-. 

 logT(a). Hermite, C. Crelle J. Mth. 115 



(1895) 201-. 

 Tin). Dixon, A. C. [1898] Mth. Gz. 1 



(1900) 189-. 

 1/r (fj.) , integral expression for. Jdrgensen, N. 



N. Ts. Mth. 11 (B) (1900) 34-; Fschr. Mth. 



(1900) 440. 



4420 Legendre's functions; Bes- 

 sel's functions ; hypergeometric 

 functions. 



Algebraic functions, class, special, arising from 

 expansion of (1 - 2xz + z 2 )*. Jacobi, C. G. J. 



Crelle J. 2 (1827) 223-. 



342 



