4400 Other Special Functions. General Eulerian Functions 4410 



Functions representable by Heine's series. 

 Thomae, J. [1868] Crelle J. 70 (1869) 258-. 



of real variables possessing distributive 

 property. Volpi, R. G. Mt. 35 (1897) 104-. 



2 variables arising from inversion of 

 integrals of two given functions. Fuchs, L. 

 Gott. Ab. 27 (1881) 39 pp. 



Higher sines of 4th order 



En zv .+n 

 T - r 

 ! M + n! 



-, 



4) . 



'J 



Kapteyn, J. C., & Kapteyn, W. Amst. Ak. 



Vh. 24 (1886) 98 pp. 

 nth order. Kapteyn, J. C., <& Kapteyn, 



W. Wien Ak. Sb. 93 (1886) (Ab. 2) 807-. 

 Infinite group of rational integral functions 



Berger, A. Stockh. Ofv. (1899) 175-. 

 Integral derived from continued fraction, 

 theorem of Hermite. Gegenbauer, L. Wien 

 Ak. Sb. 92 (1886) (Ab. 2) 995-. 



transcendental functions, distribution of 

 roots of class. Bukreev, B. Ja. [1893] Eec. 

 Mth. (Moscou) 17 (1895) 217- ; Fschr. Mth. 

 (1893-94) 678. 



Iterative functions. Farkas, J. Liouv. J. 



Mth. 10 (1884) 101-. 



. Netto, E. Mth. A. 29 (1887) 148-. 



, differential coefficients, at limiting point. 



Lemeray, . Par. S. Mth. Bll. 25 (1897) 51-. 

 , theorem. Lemeray, . Par. S. Mth. 



Bll. 23 (1895) 255-. 



in theory of integral transcendental 

 functions. Hill, C. J. D. Crelle J. 11 

 (1834) 193-. 



Prym's function, generalisation. Nielsen, N. 



N. Ts. Mth. 11 (B) (1900) 73-; Fschr. Mth. 



(1900) 440-. 

 Pseudo- and hyper-Bernoullian functions and 



their applications. Lang champs, G. de. 



Brux. Mm. Cour. 4, 52 (1890-93) No. 1, 



41 pp. 



n fn\ 



Eecurring function c n S (-!)"( ) c . 



o vy 



Lerch, M. Casopis 22 (1893) 31-; Fschr. 



Mth. (1893-94) 409-. 

 Eepeated exponentials. Grave, D. N. A. 



Mth. 17 (1898) 80-. 

 Eiemann's f(s) function, generalisation. 



Mellin, H. Helsingf. Acta 24 (1899) No. 10, 



50pp. 

 for odd values of argument. Lerch, M. 



G. Teix. J. Sc. 14 (1900) 65-. 

 Theorem of Stieltjes, and functions denned by 



continued fractions. Koch, H. von. Par. 



S. Mth. Bll. 23 (1895) 33-. 

 Transcendental function, new. Soldner, J. 



Zach M. Cor. 23 (1811) 182-. 

 , , in relation with functions T and Z. 



Blaserna, P. Em. E. Ac. Line. Mm. 1 (1894) 



499-. 



functions. Broch, 0. J. Crelle J. 20 

 (1840) 178- ; N. Mg. Ntvd. 2 (1840) 297-. 



with algebraic differentials. Hermite, C. 



C. E. 18 (1844) 1133-. 



Transcendental functions, arithmetical pro- 

 perty. Hurwitz, A. Mth. A. 32 (1888) 583-. 

 -, case. Holder, O. Gott. Nr. (1886) 514-. 



, classification ; and general^, theory of 

 integration. Drach, J. Par. EC. Norm. 

 A. 15 (1898) 243-. 



, comparison. Boole, G. Phil. Trans. 

 (1857) 745-. 



, theorem of Sturm. Liouville, J. 



Liouv. J. Mth. 1 (1836) 269-. 

 , Z' (a) and Ga, and calculation of their 



values for several values of a. Lindman, 



C. F. [1863] Stockh. Ak. Hndl. 5 (1866) 



No. 2, 18 pp. 



quantities. Liouville, J. Liouv. J. Mth. 

 16 (1851) 133-. 



Transcendentally transcendental functions. 



Moore, E. H. Mth. A. 48 (1897) 49-. 

 Trigonometric null-representations, special 



class. Rogel, F. Arch. Mth. Ps. 15 (1897) 



431-. 



(x'~v p ~ 1 F(x)(R(xf))*vdx. Broch, O.J. 

 Crelle J. 23 (1842) 145-, 201-. 



a a ' , development. Eisenstein, G. Crelle J. 28 

 (1844) 49-. 



and corresponding invert functions. 

 Woepcke, F. Crelle J. 42 (1851) 83-. 



z*. Le Cointe, J. L. A. (vm) A. Mt. 5 (1863) 



106-. 

 2e zknix l(w + k)*, k = Q to oo . Lerch, M. Acta 



Mth. 11 (1887-88) 19-. 

 (f n (x). Gegenbauer, L. Wien Ak. Sb. 97 



(1889) (Ab. 2a) 259-. 

 , addition theorem. Gegenbauer, L. Wien 



Ak. Sb. 102 (1893) (Ab. 2a) 942-. 

 y defined by 2a rs x r y a = Q. Melander, K. 



Fschr. Mth. (1890) 409. 



S ( . h ( - w) m - cot ) , new form of 



\sinrz<T7r v 'a <j ) 

 analytical expression. Lerch, M. Prag 

 Ceske Ak. Fr. Jos. Ez. (Tflda 2) 9 (1900) 

 Art. 6, 17 pp.; Fschr. Mth. (1900) 401-. 



4410 Eulerian functions. 



Bourguet, L. C. E. 96 (1883) 1307-. 

 Analogues to Eulerian functions. Appell, P. 



[1879-81] C. E. 86 (1878) 953-; 89 (1879) 



841-, 1031- ; Mth. A. 19 (1882) 84-. 



. Ciani, V. G. Mt. 29 (1891) 68-. 



Analytic factorials, coefficients. Gambardella, 



F. G. Mt. 11 (1873) 49-, 86-. 

 Approximate value of nl Malfatti, G. F. 



Verona S. It. Mm. 4JT788) 206-. 

 Asymptotic value of V(a) when a is great. 



Hermite, . Am. J. Mth. 17 (1895) 6-. 

 Bernoulli's theorem, gamma-function and 



Laplace's integral. Eggenberger, J. Bern 



Mt. (1893) 110- , 236. 

 Binet's formula. Genocchi, A. Brux. Ac. 



Bll. 20 (1853) (pte. 2) 392-; Tortolini A. 



5 (1854) 150-. 

 for <o(/u), generalisation. Tilly, J. M. de. 



Brux. Ac. Bll. 38 (1874) 67-. 



339 



Y2 



