@article{RSMUP_2007__118__159_0,
author = {Ernst, Thomas},
title = {Some new Formulas involving $\Gamma \_q$Functions},
journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
volume = {117},
year = {2007},
pages = {159-188},
mrnumber = {2378394},
zbl = {1165.33307},
language = {en},
url = {http://dml.mathdoc.fr/item/RSMUP_2007__118__159_0}
}
Ernst, Thomas. Some new Formulas involving $\Gamma _q$Functions. Rendiconti del Seminario Matematico della Università di Padova, Tome 117 (2007) pp. 159-188. http://gdmltest.u-ga.fr/item/RSMUP_2007__118__159_0/
[1] , Sharp bounds for the ratio of q-gamma functions. Math. Nachr., 222 (2001), pp. 5-14. | MR 1812485 | Zbl 0968.33004
[2] , On the q-analog of Kummer's theorem and applications. Duke Math. J., 40 (1973), | MR 320375 | Zbl 0266.33003
[3] , On q-analogues of the Watson and Whipple summations. SIAM J. Math. Anal., 7 no. 3 (1976), pp. 332-336. | MR 399529 | Zbl 0339.33007
[4] - - , Special functions. Encyclopedia of Mathematics and its Applications, 71. Cambridge University Press, Cambridge, 1999. | MR 1688958 | Zbl 0920.33001
[5] , Die Heineschen O-Funktionen. Dissertation Muenchen 1909. | JFM 41.0515.02
[6] - , A q-analogue of the Euler gamma integral (Russian, English) Theor. Math. Phys., 129, no. 1 (2001), pp. 1325-1334. | MR 1904745 | Zbl 1028.33011
[7] , Generalized hypergeometric series. Cambridge 1935, reprinted by Stechert-Hafner, New York, 1964. | JFM 61.0406.01 | MR 185155 | Zbl 0011.02303
[8] , On the sum of a terminating 3F2(1). Quart. J. Math., Oxford Ser. (2) 4 (1953), pp. 237-240. | MR 57381 | Zbl 0051.30803
[9] - - , Group theoretical basis of some identities for the generalized hypergeometric series. J. Math. Phys., 28, no. 3 (1987), pp. 497-508. | MR 877220 | Zbl 0651.40003
[10] , Expansions of hypergeometric functions. Quart. J. Math., Oxford Ser., 13 (1942), pp. 159-171. | MR 7819 | Zbl 0063.00807
[11] , Basic hypergeometric series, Thesis, Lincoln, Nebraska 1941.
[12] , The history of q-calculus and a new method, Uppsala, 2000.
[13] , Some results for q-functions of many variables. Rendiconti di Padova, 112 (2004), pp. 199-235. | Numdam | MR 2109962 | Zbl 1167.33308
[14] , q-Generating functions for one and two variables. Simon Stevin, 12 no. 4 (2005), pp. 589-605. | MR 2206002 | Zbl 1132.33335
[15] , q-Bernoulli and q-Euler Polynomials, An Umbral Approach. International journal of difference equations and dynamical systems. To be published 2006. | MR 2296498 | Zbl 1116.39013
[16] , Introductio in Analysin Infinitorum, T1, Lausanne 1748.
[17] - , Basic hypergeometric series. Cambridge 1990. | MR 1052153 | Zbl 0695.33001
[18] - , Basic hypergeometric series, 2nd ed., Cambridge, 2004. | MR 2128719 | Zbl 1129.33005
[19] , Werke 2, 1876, pp. 9-45.
[20] - - , General hypergeometric systems of equations and series of hypergeometric type, Russian Math. Surveys, 47, no. 4 (1992), pp. 1-88. | MR 1208882 | Zbl 0798.33010
[21] , Elementary proofs of some q-identities of Jackson and AndrewsJain. Discrete Math., 295, no. 1-3 (2005), pp. 63-74. | MR 2139126 | Zbl 1080.33015
[22] , Beiträge zur Theorie der Heineschen Reihen. Mathematische Nachrichten, 2 (1949), pp. 340-379. | MR 35344 | Zbl 0033.05703
[23] , Über die höheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen. Mathematische Nachrichten, 3 (1950), pp. 257-294. | MR 40557 | Zbl 0038.05002
[24] , Über die Reihe... J. reine angew. Math., 32 (1846), pp. 210-212. | Zbl 032.0920cj
[25] - , Inequalities and monotonicity properties for gamma and q-gamma functions. Approximation and computation (West Lafayette, IN, 1993), pp. 309-323, Internat. Ser. Numer. Math., 119, Birkh user Boston, Boston, MA, 1994. | MR 1333625 | Zbl 0819.33001
[26] , Studier over en Afhandling af Gauss. (Studien über eine Abhandlung von Gauss.). (Danish) Nyt Tidsskr. for Math. 29 (1918), pp. 29-36. | JFM 46.0339.02
[27] - - , On q-Gauss's second summation theorem. Far East J. Math. Sci. (FJMS) 17, no. 3 (2005), pp. 299-303. | MR 2183187 | Zbl 1081.33031
[28] , Über die hypergeometrische Reihe ... J. für Math., 15 (1836), pp. 39-83 and pp. 127-172. | Zbl 015.0533cj
[29] , q-Newton Binomial: from Euler to Gauss, J. Nonlinear Math. Phys. 7, no. 2 (2000), pp. 244-262. | MR 1763640 | Zbl 0955.33012
[30] , Sulle Funzioni Ipergeometriche a più Variabili. Rend. Circ. Mat. Palermo, 7 (1893), pp. 111-158. | JFM 25.0756.01
[31] , Abriss einer einheitlichen Theorie der Gamma und der hypergeometrischen Funktionen. Mathematische Annalen, 68 (1910), pp. 305-337. | JFM 41.0500.04 | MR 1511564
[32] , Sopra un procedimento di calcolo analogo alla integrazione. (Italian) Palermo Rend., 47 (1923), 337-374 | JFM 49.0196.02
[33] , Asymptotic expansions for q-gamma, q-exponential, and q-Bessel functions. J. Math. Anal. Appl., 186, no. 3 (1994), 896-913. | MR 1293861 | Zbl 0809.33008
[34] , Some multiple series transformations. J naÅnabha Sect. A 4 (1974) 165-168. | MR 382745 | Zbl 0297.33023
[35] - - , A=B, A.K. Peters 1996. | MR 1379802
[36] , Special functions, Bronx, N.Y., 1971. | MR 393590 | Zbl 0231.33001
[37] , On the reducibility of Lauricella's function FD. J naÅnabha A 4 (1974), pp. 163-164. | MR 382744 | Zbl 0281.33012
[38] - - - - , Group theoretical basis for the terminating 3F2(1) series. J. Phys. A, 25, no. 4 (1992), pp. 861-876. | MR 1151088 | Zbl 0761.33002
[39] , Sums of a certain class of q-series. Proc. Japan Acad. Ser. A Math. Sci., 65, no. 1 (1989), pp. 8-11 | MR 1011827 | Zbl 0653.33004
[40] , Les séries Heinéennes supérieures. Ann. Mat. pura appl. Bologna, II 4 (1871), pp. 105-139. | JFM 03.0108.01
[41] , Abriss einer Theorie der Functionen einer complexen Veraenderlichen und der Thetafunctionen. Zweite vermehrte Auflage. Halle a. S. Nebert. (1873). | JFM 05.0218.01
[42] , Über die Funktionen welche durch Reihen von der Form dargestellt werden: J. reine angew. Math., 87 (1879), pp. 26-73.
[43] - , Invariance groups of transformations of basic hypergeometric series. J. Math. Phys. 40, no. 12 (1999), pp. 6692-6700. | MR 1725881 | Zbl 0956.33012
[44] , A Calculus of Sequences, Amer. J. Math., 58 (1936), pp. 255-266. | JFM 62.0408.03 | MR 1507149
[45] , A note on generalized hypergeometric series. Proceedings L. M. S. (2) 23, XIII-XV. (1925) | JFM 51.0283.04
[46] , A new proof of the Rogers-Ramanujan identities. J. London Math. Soc. 4 (1929), pp. 4-9. | JFM 55.0219.09
[47] , The final problem: an account of the mock theta functions. J. London Math. Soc. 11 (1936), pp. 55-80. | JFM 62.0430.02 | MR 1862757
[48] , A group of generalized hypergeometric series: relations between 120 allied series of the type 3F2(a; b; c; d; e). Proc. London Math. Soc. (2) 23 (1925), pp. 104-114. | JFM 50.0259.02