Multiple Gamma and related functions

Applied Mathematics and Computation

Volumn 134, Issue 2-3, 2002, Pages 515-533

  Choi, Junesang ^a   Srivastava, H M ^b   Adamchik, V S ^c  

^a Dongguk University   (South Korea)

^b UNIVERSITY OF VICTORIA   (Canada)

^c Carnegie Mellon University ^*  (United States)

Author keywords

Clausen integrals; Determinants of Laplacians; Hurwitz Zeta function; Multiple Gamma functions; Riemann's function; Series involving the Zeta function

Indexed keywords

EID: 0037169623     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(01)00301-0     Document Type: Article

References (42)

1. V.S. Adamchik Polygamma functions of negative order J. Comput. Appl. Math. 100 1998 191 199
2. V.S. Adamchik, Integral representations for the Barnes function, 2001 (Preprint)
3. V.S. Adamchik, On the Barnes function, in: B. Mourrain (Ed.), Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, London, July 22–25, 2001, ACM Press, New York, 2001, pp. 15–20
4. V.S. Adamchik H.M. Srivastava Some series of the Zeta and related functions Analysis 18 1998 131 144
5. W.P. Alexeiewsky Über eine Classe von Funktionen, die der Gammafunktion analog sind Leipzig Weidmannsche Buchhandlung 46 1894 268 275
6. R. Ayoub Euler and the Zeta function Amer. Math. Monthly 81 1974 1067 1086
7. E.W. Barnes The theory of the G -function Quart. J. Math. 31 1899 264 314
8. E.W. Barnes On the theory of the multiple Gamma function Trans. Cambridge Philos. Soc. 19 1904 374 439
9. L. Bendersky Sur la fonction Gamma généralisée Acta Math. 61 1933 263 322
10. M.-P. Chen H.M. Srivastava Some families of series representations for the Riemann ζ (3) Resultate Math. 33 1998 179 197
11. 3 Math. Japon. 40 1994 155 166
12. J. Choi Explicit formulas for Bernoulli polynomials of order n Indian J. Pure Appl. Math. 27 1996 667 674
13. J. Choi C. Nash Integral representations of the Kinkelin's constant A Math. Japon. 45 1997 223 230
14. J. Choi T.Y. Seo The double Gamma function East Asian Math. J. 13 1997 159 174
15. J. Choi H.M. Srivastava Sums associated with the Zeta function J. Math. Anal. Appl. 206 1997 103 120
16. J. Choi H.M. Srivastava Certain classes of series involving the Zeta function J. Math. Anal. Appl. 231 1999 91 117
17. J. Choi H.M. Srivastava An application of the theory of the double Gamma function Kyushu J. Math. 53 1999 209 222
18. J. Choi H.M. Srivastava Certain classes of series associated the Zeta function and multiple Gamma functions J. Comput. Appl. Math. 118 2000 87 109
19. J. Choi H.M. Srivastava J.R. Quine Some series involving the Zeta function Bull. Austral. Math. Soc. 51 1995 383 393
20. D. Cvijović J. Klinowski Closed-form summation of some trigonometric series Math. Comput. 64 1995 205 210
21. A. Erdélyi W. Magnus F. Oberhettinger F.G. Tricomi Higher Transcendental Functions Vol. I 1953 McGraw-Hill New York
22. n Messenger Math. 7 1877 43 47
23. m/6 ln Γ(z) d z Fields Inst. Comm. 14 1997 71 76
24. I.S. Gradshteyn I.M. Ryzhik Table of Integrals, Series, and Products 1980 Academic Press New York (Corrected and Enlarged Ed. prepared by A. Jeffrey)
25. 2( θ ) J. Comput. Appl. Math. 11 1984 331 342
26. E.R. Hansen A Table of Series and Products 1975 Prentice-Hall Englewood Cliffs, NJ
27. S. Kanemitsu H. Kumagai M. Yoshimoto Sums involving the Hurwitz Zeta function Ramanujan J. 5 2001 5 19
28. L. Lewin Polylogarithms and Associated Functions 1981 Elsevier Amsterdam
29. A.P. Prudnikov, Yu.A. Bryčkov, O.I. Maričev, Integrals and Series (Elementary Functions), Nauka, Moscow, 1981 (in Russian); see also Integrals and Series, Vol. I: Elementary Functions (Translated from the Russian by N.M. Queen), Gordon and Breach, New York, 1986
30. J.R. Quine J. Choi Zeta regularized products and functional determinants on spheres Rocky Mountain J. Math. 26 1996 719 729
31. M.R. Spiegel Mathematical Handbook 1968 McGraw-Hill New York
32. H.M. Srivastava A unified presentation of certain classes of series of the Riemann Zeta function Riv. Mat. Univ. Parma 4 14 1988 1 23
33. H.M. Srivastava Some rapidly converging series for ζ (2 n +1) Proc. Amer. Math. Soc. 127 1999 385 396
34. H.M. Srivastava A note on the closed-form summation of some trigonometric series Kobe J. Math. 16 1999 177 182
35. H.M. Srivastava Some simple algorithms for the evaluations and representations of the Riemann Zeta function at positive integer arguments J. Math. Anal. Appl. 246 2000 331 351
36. H.M. Srivastava J. Choi Series Associated with the Zeta and Related Functions 2001 Kluwer Academic Publishers Dordrecht
37. H.M. Srivastava M.L. Glasser V.S. Adamchik Some definite integrals associated with the Riemann Zeta function Z. Anal. Anwendungen 19 2000 831 846
38. E.C. Titchmarsh The Theory of the Riemann Zeta-Function Second Ed. 1951 Clarendon Press Oxford (Revised by D.R. Heath-Brown, 1986)
39. I. Vardi Determinants of Laplacians and multiple Gamma functions SIAM J. Math. Anal. 19 1988 493 507
40. M.-F. Vignéras L'équation fonctionnelle de la fonction Zêta de Selberg du groupe moudulaire PSL (2, Z ) Journées Arithmétiques de Luminy, Colloq. Internat. CNRS, Centre Univ. Luminy, Luminy, 1978 Astérisque 61 1979 Soc. Math. France Paris 235 249
41. A. Voros Special functions, spectral functions and the Selberg Zeta function Comm. Math. Phys. 110 1987 439 465
42. E.T. Whittaker G.N. Watson A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; With an Account of the Principal Transcendental Functions Fourth Ed. 1963 Cambridge University Press Cambridge