Some classes of infinite series associated with the Riemann Zeta and Polygamma functions and generalized harmonic numbers

Applied Mathematics and Computation

Volumn 131, Issue 2-3, 2002, Pages 593-605

  Rassias, Themistocles M ^a   Srivastava, H M ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Fractional calculus; Gauss summation theorem; Generalized harmonic numbers; Polygamma functions; Riemann Zeta function; Stirling numbers of the first kind

Indexed keywords

EID: 0037174278     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(01)00172-2     Document Type: Article

References (21)

1. B.N. Al-Saqabi S.L. Kalla H.M. Srivastava A certain family of infinite series associated with Digamma functions J. Math. Anal. Appl. 159 1991 361 372
2. J. Aular de Durán S.L. Kalla H.M. Srivastava Fractional calculus and the sums of certain families of infinite series J. Math. Anal. Appl. 190 1995 738 754
3. B.C. Berndt Ramanujan's Notebooks, Part I 1985 Springer New York
4. D. Borwein J.M. Borwein On an intriguing integral and some series related to ζ (4) Proc. Amer. Math. Soc. 123 1995 1191 1198
5. K.-Y. Chen H.M. Srivastava Some infinite series and functional relations that arose in the context of fractional calculus J. Math. Anal. Appl. 252 2000 376 388
6. 2 for certain values of x and y J. Comput. Appl. Math. 37 1991 125 141
7. A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, vol. I, McGraw-Hill, New York, 1953
8. R.L. Graham D.E. Knuth O. Patashnik Concrete Mathematics 1989 Addison-Wesley Reading, MA
9. E.R. Hansen A Table of Series and Products 1975 Prentice-Hall Englewood Cliffs, NJ
10. C. Jordan Calculus of Finite Differences Third Edition 1965 Chelsea New York (with Introduction by H.C. Carver)
11. L. Lewin Polylogarithms and Associated Functions 1981 Elsevier Amsterdam
12. W. Magnus, F. Oberhettinger, R.P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Third Enlarged Edition, Die Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 52, Springer, New York, 1966
13. H.A. Mavromatis Double and triple summation expressions obtained using perturbation theory Internat. J. Math. and Math. Sci. 23 2000 289 295
14. K. Nishimoto H.M. Srivastava Certain classes of infinite series summable by means of fractional calculus J. College Engrg. Nihon Univ. Ser. B 30 1989 97 106
15. A.P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series, vol. 1: Elementary Functions, Nauka, Moscow, 1981 (in Russian); Gordon and Breach, New York, 1986 (in English)
16. J. Riordan Combinatorial Identities 1968 Wiley New York
17. H.F. Sandham M. Kneser A summation problem Amer. Math. Monthly 57 1950 267 268
18. L.-C. Shen Remarks on some integrals and series involving the Stirling numbers and ζ ( n ) Trans. Amer. Math. Soc. 347 1995 1391 1399
19. H.M. Srivastava A simple algorithm for the evaluation of a class of generalized hypergeometric series Stud. Appl. Math. 86 1992 79 86
20. H.M. Srivastava, J. Choi, Series Associated with the Zeta and Related Functions, Kluwer, Dordrecht, 2001
21. T.-C. Wu S.-H. Leu S.-T. Tu H.M. Srivastava A certain class of infinite sums associated with Digamma functions Appl. Math. Comput. 105 1999 1 9