메뉴 건너뛰기




Volumn 141, Issue 1, 2003, Pages 13-49

Certain classes of series associated with the Zeta and related functions

Author keywords

Bernoulli numbers; Bernoulli polynomials; Dirichlet's L functions; Euler numbers; Euler polynomials; Generating functions; Harmonic numbers; Hurwitz (or generalized) Zeta function; Riemann Zeta function; Series representations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NUMBER THEORY; POLYNOMIALS; PROBLEM SOLVING;

EID: 0037457771     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(02)00318-1     Document Type: Conference Paper
Times cited : (18)

References (42)
  • 1
    • 0000455331 scopus 로고    scopus 로고
    • Some series of the Zeta and related functions
    • Adamchik V.S., Srivastava H.M. Some series of the Zeta and related functions. Analysis. 18:1998;131-144.
    • (1998) Analysis , vol.18 , pp. 131-144
    • Adamchik, V.S.1    Srivastava, H.M.2
  • 2
    • 0001934611 scopus 로고
    • Irrationalité de ζ (2) et ζ (3), in Journées Arithmétiques de Luminy
    • (Colloq. Internat. CNRS, Centre Univ. Luminy, Luminy, 1978), Soc. Math. France, Paris
    • R. Apéry, Irrationalité de ζ (2) et ζ (3), in Journées Arithmétiques de Luminy (Colloq. Internat. CNRS, Centre Univ. Luminy, Luminy, 1978), Astérisque 61, Soc. Math. France, Paris, 1979, pp. 11-13.
    • (1979) Astérisque , vol.61 , pp. 11-13
    • Apéry, R.1
  • 3
    • 0000428944 scopus 로고
    • Euler and the Zeta function
    • Ayoub R. Euler and the Zeta function. Amer. Math. Monthly. 81:1974;1067-1086.
    • (1974) Amer. Math. Monthly , vol.81 , pp. 1067-1086
    • Ayoub, R.1
  • 5
    • 0012662556 scopus 로고    scopus 로고
    • Some families of series representations for the Riemann ζ(3)
    • Chen M.-P., Srivastava H.M. Some families of series representations for the Riemann. ζ(3) Resultate Math. 33:1998;179-197.
    • (1998) Resultate Math. , vol.33 , pp. 179-197
    • Chen, M.-P.1    Srivastava, H.M.2
  • 6
    • 21744449094 scopus 로고    scopus 로고
    • New rapidly convergent series representations for ζ(2n+1)
    • Cvijović D., Klinowski J. New rapidly convergent series representations for. ζ(2n+1) Proc. Amer. Math. Soc. 125:1997;1263-1271.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 1263-1271
    • Cvijović, D.1    Klinowski, J.2
  • 7
    • 0012754312 scopus 로고    scopus 로고
    • A note on the values of the Riemann Zeta function at positive odd integers
    • Da̧browski A. A note on the values of the Riemann Zeta function at positive odd integers. Nieuw Arch. Wisk. 4(14):1996;199-207.
    • (1996) Nieuw Arch. Wisk. , vol.4 , Issue.14 , pp. 199-207
    • Da̧browski, A.1
  • 9
    • 0000833825 scopus 로고
    • A new series representation for ζ(3)
    • Ewell J.A. A new series representation for. ζ(3) Amer. Math. Monthly. 97:1990;219-220.
    • (1990) Amer. Math. Monthly , vol.97 , pp. 219-220
    • Ewell, J.A.1
  • 10
    • 84881277236 scopus 로고
    • On the Zeta function values ζ(2k+1), k=1,2, ...
    • Ewell J.A. On the Zeta function values. ζ(2k+1), k=1,2,..., Rocky Mountain J. Math. 25:1995;1003-1012.
    • (1995) Rocky Mountain J. Math. , vol.25 , pp. 1003-1012
    • Ewell, J.A.1
  • 11
    • 84968499547 scopus 로고
    • Some integrals of the arctangent function
    • Glasser M.L. Some integrals of the arctangent function. Math. Comput. 22:1968;445-447.
    • (1968) Math. Comput. , vol.22 , pp. 445-447
    • Glasser, M.L.1
  • 12
    • 0012719129 scopus 로고
    • A calculus of series rearrangements
    • J.F. Traub. New York, London, and Toronto: Academic Press
    • Gosper R.W. Jr. A calculus of series rearrangements. Traub J.F. Algorithms and Complexity: New Directions and Recent Results. 1976;121-151 Academic Press, New York, London, and Toronto.
    • (1976) Algorithms and Complexity: New Directions and Recent Results , pp. 121-151
    • Gosper R.W., Jr.1
  • 15
    • 0004024987 scopus 로고
    • New York, Chichester, Brisbane, and Toronto: John Wiley and Sons
    • Ivić A. The Riemann Zeta-Function. 1985;John Wiley and Sons, New York, Chichester, Brisbane, and Toronto.
    • (1985) The Riemann Zeta-Function
    • Ivić, A.1
  • 16
    • 0001799697 scopus 로고    scopus 로고
    • Rapidly convergent series representations for ζ(2n+1) and their χ -analogue
    • Katsurada M. Rapidly convergent series representations for. ζ(2n+1) and their χ -analogue Acta Arith. 40:1999;79-89.
    • (1999) Acta Arith. , vol.40 , pp. 79-89
    • Katsurada, M.1
  • 19
    • 0012701681 scopus 로고
    • Ray-Singer torsion, topological field theories and the Riemann Zeta function at s=3
    • H. Osborn (Ed.), Proceedings of a NATO Advanced Research Workshop held at the Isaac Newton Institute at Cambridge, UK, 6-12 September 1992, Plenum Press, New York and London
    • C. Nash, D. O'Connor, Ray-Singer torsion, topological field theories and the Riemann Zeta function at s=3, in: H. Osborn (Ed.), Low-Dimensional Topology and Quantum Field Theory, Proceedings of a NATO Advanced Research Workshop held at the Isaac Newton Institute at Cambridge, UK, 6-12 September 1992, Plenum Press, New York and London, 1993, pp. 279-288.
    • (1993) Low-Dimensional Topology and Quantum Field Theory , pp. 279-288
    • Nash, C.1    O'Connor, D.2
  • 20
    • 21844509292 scopus 로고
    • Determinants of Laplacians, the Ray-Singer torsion on lens spaces and the Riemann Zeta function
    • Nash C., O'Connor D. Determinants of Laplacians, the Ray-Singer torsion on lens spaces and the Riemann Zeta function. J. Math. Phys. 36:1995;1462-1505.
    • (1995) J. Math. Phys. , vol.36 , pp. 1462-1505
    • Nash, C.1    O'Connor, D.2
  • 21
    • 84963015857 scopus 로고
    • Notes on Riemann's ζ -function
    • Ramaswami V. Notes on Riemann's. ζ -function J. London Math. Soc. 9:1934;165-169.
    • (1934) J. London Math. Soc. , vol.9 , pp. 165-169
    • Ramaswami, V.1
  • 23
    • 0002676205 scopus 로고
    • A unified presentation of certain classes of series of the Riemann Zeta function
    • Srivastava H.M. A unified presentation of certain classes of series of the Riemann Zeta function. Riv. Mat. Univ. Parma. 4(14):1988;1-23.
    • (1988) Riv. Mat. Univ. Parma , vol.4 , Issue.14 , pp. 1-23
    • Srivastava, H.M.1
  • 24
    • 38249026905 scopus 로고
    • Sums of certain series of the Riemann Zeta function
    • Srivastava H.M. Sums of certain series of the Riemann Zeta function. J. Math. Anal. Appl. 134:1988;129-140.
    • (1988) J. Math. Anal. Appl. , vol.134 , pp. 129-140
    • Srivastava, H.M.1
  • 25
    • 0002094881 scopus 로고    scopus 로고
    • Certain families of rapidly convergent series representations for ζ(2n+1)
    • (Research Announcement)
    • Srivastava H.M. Certain families of rapidly convergent series representations for. ζ(2n+1) Math. Sci. Res. Hot-Line. 1(6):1997;1-6. (Research Announcement).
    • (1997) Math. Sci. Res. Hot-Line , vol.1 , Issue.6 , pp. 1-6
    • Srivastava, H.M.1
  • 26
    • 0012754313 scopus 로고    scopus 로고
    • Further series representations for ζ(2n+1)
    • Srivastava H.M. Further series representations for. ζ(2n+1) Appl. Math. Comput. 97:1998;1-15.
    • (1998) Appl. Math. Comput. , vol.97 , pp. 1-15
    • Srivastava, H.M.1
  • 27
    • 22444452320 scopus 로고    scopus 로고
    • Some rapidly converging series for ζ(2n+1)
    • Srivastava H.M. Some rapidly converging series for. ζ(2n+1) Proc. Amer. Math. Soc. 127:1999;385-396.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , pp. 385-396
    • Srivastava, H.M.1
  • 28
    • 0012669826 scopus 로고    scopus 로고
    • Some simple algorithms for the evaluations and representations of the Riemann Zeta function at positive integer arguments
    • Srivastava H.M. 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.
    • (2000) J. Math. Anal. Appl. , vol.246 , pp. 331-351
    • Srivastava, H.M.1
  • 30
    • 23044522077 scopus 로고    scopus 로고
    • Some definite integrals associated with the Riemann Zeta function
    • Srivastava H.M., Glasser M.L., Adamchik V.S. Some definite integrals associated with the Riemann Zeta function. Z. Anal. Anwendungen. 19:2000;831-846.
    • (2000) Z. Anal. Anwendungen , vol.19 , pp. 831-846
    • Srivastava, H.M.1    Glasser, M.L.2    Adamchik, V.S.3
  • 31
    • 0012721914 scopus 로고    scopus 로고
    • A certain class of rapidly convergent series representations for ζ(2n+1)
    • Srivastava H.M., Tsumura H. A certain class of rapidly convergent series representations for. ζ(2n+1) J. Comput. Appl. Math. 118:2000;323-335.
    • (2000) J. Comput. Appl. Math. , vol.118 , pp. 323-335
    • Srivastava, H.M.1    Tsumura, H.2
  • 32
    • 0012741232 scopus 로고    scopus 로고
    • New rapidly convergent series representations for ζ(2n+1), L(2n,χ) and L(2n+1,χ)
    • (Research Announcement)
    • Srivastava H.M., Tsumura H. New rapidly convergent series representations for. ζ(2n+1), L(2n,χ) and L(2n+1,χ) Math. Sci. Res. Hot-Line. 4(7):2000;17-24. (Research Announcement).
    • (2000) Math. Sci. Res. Hot-Line , vol.4 , Issue.7 , pp. 17-24
    • Srivastava, H.M.1    Tsumura, H.2
  • 33
    • 0041032482 scopus 로고    scopus 로고
    • Certain classes of rapidly convergent series representations for L(2n,χ) and L(2n+1,χ)
    • Srivastava H.M., Tsumura H. Certain classes of rapidly convergent series representations for. L(2n,χ) and L(2n+1,χ) Acta Arith. 100:2001;195-201.
    • (2001) Acta Arith. , vol.100 , pp. 195-201
    • Srivastava, H.M.1    Tsumura, H.2
  • 35
    • 0003669011 scopus 로고
    • Oxford University (Clarendon) Press, Oxford and London, second ed., revised by D.R. Heath-Brown, 1986
    • E.C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford University (Clarendon) Press, Oxford and London, 1951; second ed., revised by D.R. Heath-Brown, 1986.
    • (1951) The Theory of the Riemann Zeta-Function
    • Titchmarsh, E.C.1
  • 36
    • 0012702410 scopus 로고
    • Sulla somma delle inverse delle terze e quinte potenze dei numeri naturali
    • Tricomi F.G. Sulla somma delle inverse delle terze e quinte potenze dei numeri naturali. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 8(47):1969;16-18.
    • (1969) Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. , vol.8 , Issue.47 , pp. 16-18
    • Tricomi, F.G.1
  • 37
    • 0000894249 scopus 로고
    • On evaluation of the Dirichlet series at positive integers by q-calculation
    • Tsumura H. On evaluation of the Dirichlet series at positive integers by q-calculation. J. Number Theory. 48:1994;383-391.
    • (1994) J. Number Theory , vol.48 , pp. 383-391
    • Tsumura, H.1
  • 40
    • 0001847762 scopus 로고
    • A proof of Burnside's formula for logΓ(x+1) and certain allied properties of Riemann's ζ -function
    • J.R. Wilton, A proof of Burnside's formula for logΓ(x+1) and certain allied properties of Riemann's ζ -function, Messenger Math. 52 (1922-1923) 90-93.
    • (1922) Messenger Math. , vol.52 , pp. 90-93
    • Wilton, J.R.1
  • 41
    • 0242310336 scopus 로고
    • On quantum gauge theories in two dimensions
    • Witten E. On quantum gauge theories in two dimensions. Comm. Math. Phys. 141:1991;153-209.
    • (1991) Comm. Math. Phys. , vol.141 , pp. 153-209
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.