4410 Eulerian Integrals 



Coefficients in differential formulae, determina- 

 tion and application to Eulerian integrals. 

 Zurria, G. Catania At. Ac. Gioen. 10 

 (1854) 265-. 



Dirichlet's formula, application to mechanics. 

 Clariana Ricart, L. Fschr. Mth. (1900) 687. 



Eulerian functions, and Bernoulli's functions. 

 Brioschi, F. (vi Adds,) Tortolini A. 1 

 (1858) 260-. 



of 2nd kind, properties. Gasparis, A. de. 



Nap. Ed. 1 (1852) 97-. 



Eulerian integrals. 



Bellavitis, G. A. Sc. Lomb. Ven. 4 (1834) 



10-. 



Lejeune-Dirichlet, G. Crelle J. 15 (1836) 258-. 

 Stern, M. A. Crelle J. 21 (1840) 377-. 

 Cauchy, A. L. C. B. 17 (1843) 376-; 19 



(1844) 67-. 

 Zhbikovskil, A. K. [1867] (XH) Kazan Un. 



Mm. 3 (1866) 212- ; (App. 3) i-. 

 Bourguet, L. Acta Mth. 1 (1882) 295-; C. E. 



96 (1883) 1487-. 

 Tannery, J. C. E. 94 (1882) 1698- ; 95 (1882) 



75. 

 application of binomial theorem. Catalan, E. C. 



C. E. 47 (1858) 545-. 



to series. Binet, J. P. M. Par. EC. Pol. J. 

 27 e cah. (1839) 123-. 



calculation by common algebraic substitution. 



Pdnek, A. Prag Sb. (1893) (Mth.-Nt.) No. 



21, 5 pp.; Fschr. Mth. (1893-94) 474. 

 cases. Dedekind, E. Crelle J. 45 (1853) 370-. 

 . Walton, W. [1872] QJ. Mth. 12 (1873) 



192. 



. Enneper, A. Gott. Nr. (1885) 163-. 

 . Pdnek, A. Prag Ceske" Ak. Fr. Jos. Ez. 



(Trida 2) 2 (1893) Art. 17, 7 pp. ; Fschr. 



Mth. (1893-94) 474. 

 and the constant G. Catalan, E. C. [1882] 



St Pet. Ac. Sc. Mm. 31 (1883) No. 3, 51 pp. 



elliptic functions. Lerch, M. Prag Sb. 

 (1897) (Mth.-Nt.) No. 28, 11 pp. 



expansion in series. Bourguet, L. Par. EC. 



Norm. A. 10 (1881) 175-. 

 expressions related to. Lerch, M. Prag Sb. 



(1890) 1 (Mth.-Nt.) 137-. 

 formulae. Catalan, E. C. [1877] Brux. Ac. 



Sc. Mm. 42 (1878) (No. 4) 20 pp. ; As. Fr. 



C. E. (1884) (Pt. 2) 11-. 

 fundamental properties. Lerch, M. Prag Sb. 



(1889) 2 (Mth.-Nt.) 188- ; Fschr. Mth. (1889) 



447-. 

 1st kind. Eealis, S. G. Mt. 9 (1871) 345-. 



. Beaupain, J. Par. EC. Norm. A. 

 9 (1892) 309- ; Brux. Mm. Cour. 4, 53 

 (1893-94) No. 1, 18 pp. 



, fundamental property, new demonstra- 

 tion. Lerch, . Par. S. Mth. Bll. 15 

 (1887) 173-. 



and 2nd kinds. Matthiessen, L. A. Mt. 

 2 U868-69) 21-. 



2nd kind. Gohierre de Longchamps, . Par. 



EC. Norm. A. 9 (1880) 419-. 

 . Gylden, J. A. H. C. E. 92 (1881) 



897-, 942-. 



Gamma Functions 4410 



2nd kind. Hermite, C. Crelle J. Mth. 90 

 (1881) 332-. 



, expansion in series of expressions de- 

 pending on. Winckler, A. Wien Ak. Sb. 

 85 (1882) (Ab. 2) 1039-. 



, formula, demonstration. Hermite, C. 

 Prag Sb. (1888) (Mth.-Nt.) 364-. 



multiple integral reducible to. Pochhammer, L. 



Crelle J. Mth. 107 (1891) 246-. 

 relation between the two. Mansion, . Brux. 



S. Sc. A. 19 (1895) (Pt. 1) 1-. 

 and series. Catalan, E. C. Brux. Ac. Bll. 



17 (1889) 129-. 



sinusoid spirals p n = ^~- cos n<f> . Loria, 



G. Prag Sb. (1897) (Mth.-Nt.) No. 18, 6 pp. 

 tables. Bellavitis, G. [1873] Ven. I. Mm. 



18 (1874) 125-. 



theorem, demonstration. Hoppe, E. Arch. 



Mth. Ps. 41 (1864) 65-. 

 theorems. Catalan, E. Brux. Ac. Bll. 22 



(1891) 459-. 

 theory. Schaar, M. Brux. Mm. Cour. 4, 22 



(1846-47) 16 pp. 



. Stern, M. A. Gott. Stud. (1847) 283-. 

 . Pochhammer, L. Mth A. 35 (1890) 495-. 

 , explanation. PreobraZenskij , P. V. Mosc. 



S. Sc. Bll. 65 (No. 2) (1890) 55-. 

 , formula, fundamental. Tortolini, B. 



Tortolini A. 5 (1854) 292-. 

 , formulae. Serret, J. A. Liouv. J. Mth. 



8 (1843) 489-. 

 and other uniform functions. Bourguet, L. 



Acta Mth. 2 (1883) 261-. 

 with unlimited argument. Hankel, H. Z. 



Mth. Ps. 9 (1864) 1-. 



Euler's constant. Lerch, M. G. Teix. J. Sc. 



13 (1897) 129-. 

 and Binet's function. Catalan, E. C. 



C. B. 77 (1873) 198- ; Liouv. J. Mth. 1 



(1875) 209-. 

 , expressions for. Lerch, M. Prag Sb. 



(1897) (Mth.-Nt.) No. 42, 5 pp. 

 E, calculation. Shanks, W. [1867-71] 



E. S. P. 15 (1867) 429-; 16 (1868) 154, 299-; 



18 (1870) 49 ; 20 (1872) 29-. 

 sum formula, representation of functions by. 



Lipschitz, E. Crelle J. 56 (1859) 11-. 

 Factorials, Stirling's theorem 



1 . 2 . 3 ... n=j2nTr . n n . e~ n , 

 proof. Glaisher, J. W. L. [1877] QJ. Mth. 

 15 (1878) 57-. 



Formula of Eaabe, on I log F(x + u) dx. 

 Lerch, M. G. Mt. 26 (1888) 39-. 



Gamma functions. 



Enneper, A. Schlomilch Z. 7 (1862) 189-. 

 Mellin, H. Stockh. Ofv. 40 (1883) No. 5, 3-. 

 Brunei, G. Bordeaux S. Sc. Mm. 3 (1887) 1-. 

 Mansion, P. Brux. S. Sc. A. 17 (1893) (Pt. 1) 



4-. 

 Baker, H. F. Mess. Mth. 25 (1896) 125-. 



340 



