메뉴 건너뛰기




Volumn 22, Issue 7, 2011, Pages 487-506

Integral and computational representations of the extended Hurwitz-Lerch zeta function

Author keywords

Analytic continuation; Fox wright function; Gauss hypergeometric function; General hurwitz lerch zeta function; H function; Lerch zeta function; Mellin barnes type integral representations; Mittag leffler type functions; Polylogarithmic function; Riemann zeta function

Indexed keywords


EID: 79959327160     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652469.2010.530128     Document Type: Article
Times cited : (106)

References (36)
  • 1
    • 0142164506 scopus 로고
    • The asymptotic expansion of integral functions defined by Taylor series
    • E.W. Barnes, The asymptotic expansion of integral functions defined by Taylor series, Philos. Trans. Roy. Soc. London. Ser. A 206 (1906), pp. 249-297.
    • (1906) Philos. Trans. Roy. Soc. London. Ser. A , vol.206 , pp. 249-297
    • Barnes, E.W.1
  • 2
    • 33845368302 scopus 로고
    • The H-function associated with a certain class of Feynman integrals
    • R.G. Buschman and H.M. Srivastava, The H-function associated with a certain class of Feynman integrals, J. Phys. A: Math. Gen. 23 (1990), pp. 4707-4710.
    • (1990) J. Phys. A: Math. Gen , vol.23 , pp. 4707-4710
    • Buschman, R.G.1    Srivastava, H.M.2
  • 7
    • 79955464613 scopus 로고    scopus 로고
    • A further study of general Hurwitz-Lerch zeta function
    • M. Garg, K. Jain, and S.L. Kalla, A further study of general Hurwitz-Lerch zeta function, Algebras Groups Geom. 25 (2008), pp. 311-319.
    • (2008) Algebras Groups Geom , vol.25 , pp. 311-319
    • Garg, M.1    Jain, K.2    Kalla, S.L.3
  • 8
    • 33749589040 scopus 로고    scopus 로고
    • Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta functions
    • M. Garg, K. Jain, and H.M. Srivastava, Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta functions, Integral Transforms Spec. Funct. 17 (2006), pp. 803-815.
    • (2006) Integral Transforms Spec. Funct , vol.17 , pp. 803-815
    • Garg, M.1    Jain, K.2    Srivastava, H.M.3
  • 9
    • 3042834009 scopus 로고    scopus 로고
    • On the generalized Zeta function and the generalized Lambert function
    • S.P. Goyal and R.K. Laddha, On the generalized Zeta function and the generalized Lambert function, Gan. ita Sandesh 11 (1997), pp. 99-108.
    • (1997) Gan. Ita Sandesh , vol.11 , pp. 99-108
    • Goyal, S.P.1    Laddha, R.K.2
  • 10
    • 34547453599 scopus 로고    scopus 로고
    • New properties of the hypergeoemtric series associated with Feynman integrals
    • K.C. Gupta and R.C. Soni, New properties of the hypergeoemtric series associated with Feynman integrals, Kyungpook Math. J. 41 (2001), pp. 97-104.
    • (2001) Kyungpook Math. J , vol.41 , pp. 97-104
    • Gupta, K.C.1    Soni, R.C.2
  • 11
    • 38649091739 scopus 로고    scopus 로고
    • A class of Hurwitz-Lerch Zeta distributions and their applications in reliability
    • P.L. Gupta, R.C. Gupta, S.-H. Ong, and H.M. Srivastava, A class of Hurwitz-Lerch Zeta distributions and their applications in reliability, Appl. Math. Comput. 196 (2008), pp. 521-531.
    • (2008) Appl. Math. Comput , vol.196 , pp. 521-531
    • Gupta, P.L.1    Gupta, R.C.2    Ong, S.-H.3    Srivastava, H.M.4
  • 12
    • 0007270304 scopus 로고
    • New properties of hypergeometric series derivable from Feynman integrals. I: Transformation and reduction formulae
    • A.A. Inayat-Hussain, New properties of hypergeometric series derivable from Feynman integrals. I: Transformation and reduction formulae, J. Phys. A: Math. Gen. 20 (1987), pp. 4109-4117.
    • (1987) J. Phys. A: Math. Gen , vol.20 , pp. 4109-4117
    • Inayat-Hussain, A.A.1
  • 13
    • 33845372007 scopus 로고
    • Newproperties of hypergeometric series derivable from Feynman integrals. II:A generalization of the H-function
    • A.A. Inayat-Hussain, Newproperties of hypergeometric series derivable from Feynman integrals. II:A generalization of the H-function, J. Phys. A: Math. Gen. 20 (1987), pp. 4119-4128.
    • (1987) J. Phys. A: Math. Gen , vol.20 , pp. 4119-4128
    • Inayat-Hussain, A.A.1
  • 14
    • 79959371516 scopus 로고    scopus 로고
    • Extended general Hurwitz-Lerch Zeta function as Mathieu (a, λ)-series
    • submitted for publication
    • D. Jankov, T.K. Pogány, and R.K. Saxena, Extended general Hurwitz-Lerch Zeta function as Mathieu (a, λ)-series, Appl. Math. Lett., submitted for publication.
    • Appl. Math. Lett
    • Jankov, D.1    Pogány, T.K.2    Saxena, R.K.3
  • 16
    • 3042752343 scopus 로고    scopus 로고
    • Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations
    • S.-D. Lin and H.M. Srivastava, Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations, Appl. Math. Comput. 154 (2004), pp. 725-733.
    • (2004) Appl. Math. Comput , vol.154 , pp. 725-733
    • Lin, S.-D.1    Srivastava, H.M.2
  • 17
    • 33749664753 scopus 로고    scopus 로고
    • Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions
    • S.-D. Lin, H.M. Srivastava, and P.-Y. Wang, Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions, Integral Transforms Spec. Funct. 17 (2006), pp. 817-827.
    • (2006) Integral Transforms Spec. Funct , vol.17 , pp. 817-827
    • Lin, S.-D.1    Srivastava, H.M.2    Wang, P.-Y.3
  • 19
    • 3042829374 scopus 로고    scopus 로고
    • Some integral forms for a generalized Zeta function
    • K. Nishimoto, C.-E Yen, and M.-L. Lin, Some integral forms for a generalized Zeta function, J. Fract. Calc. 22 (2002), pp. 91-97.
    • (2002) J. Fract. Calc , vol.22 , pp. 91-97
    • Nishimoto, K.1    Yen, C.-E.2    Lin, M.-L.3
  • 20
    • 36949010134 scopus 로고    scopus 로고
    • A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch Zeta function
    • D. Rǎducanu and H.M. Srivastava, A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct. 18 (2007), pp. 933-943.
    • (2007) Integral Transforms Spec. Funct , vol.18 , pp. 933-943
    • Rǎducanu, D.1    Srivastava, H.M.2
  • 22
    • 77957223814 scopus 로고    scopus 로고
    • Functional relations involving generalizedH-function
    • R.K. Saxena, Functional relations involving generalizedH-function, Matematiche (Catania) 53 (1998), pp. 123-131.
    • (1998) Matematiche (Catania) , vol.53 , pp. 123-131
    • Saxena, R.K.1
  • 23
    • 79959352612 scopus 로고
    • A complex inversion theorem for a modified H-transformation of distributions, Indian
    • R.K. Saxena and N. Gupta, A complex inversion theorem for a modified H-transformation of distributions, Indian J. Pure Appl. Math. 26 (1995), pp. 1111-1117.
    • (1995) J. Pure Appl. Math , vol.26 , pp. 1111-1117
    • Saxena, R.K.1    Gupta, N.2
  • 24
    • 77957224078 scopus 로고    scopus 로고
    • On unified fractional integration operators
    • R.K. Saxena and M.K. Soni, On unified fractional integration operators, Math. Balkanica 11 (1997), pp. 69-77.
    • (1997) Math. Balkanica , vol.11 , pp. 69-77
    • Saxena, R.K.1    Soni, M.K.2
  • 25
    • 79959335404 scopus 로고    scopus 로고
    • Unified fractional integral formulas for the generalized H-function
    • R.K. Saxena, J. Ram, and S.L. Kalla, Unified fractional integral formulas for the generalized H-function, Rev. Acad. Canaria Cienc. 14 (2002), pp. 97-109.
    • (2002) Rev. Acad. Canaria Cienc , vol.14 , pp. 97-109
    • Saxena, R.K.1    Ram, J.2    Kalla, S.L.3
  • 26
    • 34547438072 scopus 로고    scopus 로고
    • Applications of the generalized H-function in bivariate distributions
    • R.K. Saxena, C. Ram, and S.L. Kalla, Applications of the generalized H-function in bivariate distributions, Rev. Acad. Canaria Cienc. 14 (2002), pp. 111-120.
    • (2002) Rev. Acad. Canaria Cienc , vol.14 , pp. 111-120
    • Saxena, R.K.1    Ram, C.2    Kalla, S.L.3
  • 27
    • 79251576218 scopus 로고    scopus 로고
    • A note on a generalzed M-series as a special function of fractional calculus
    • M. Sharma and R. Jain, A note on a generalzed M-series as a special function of fractional calculus, Fract. Calc. Appl. Anal. 12 (2009), pp. 449-452.
    • (2009) Fract. Calc. Appl. Anal , vol.12 , pp. 449-452
    • Sharma, M.1    Jain, R.2
  • 28
    • 23044520680 scopus 로고    scopus 로고
    • Some formulas for the Bernoulli and Euler polynomials at rational arguments
    • H.M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), pp. 77-84.
    • (2000) Math. Proc. Cambridge Philos. Soc , vol.129 , pp. 77-84
    • Srivastava, H.M.1
  • 31
    • 64449085065 scopus 로고    scopus 로고
    • Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel
    • H.M. Srivastava and Ž. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comput. 211 (2009), pp. 198-210.
    • (2009) Appl. Math. Comput , vol.211 , pp. 198-210
    • Srivastava, H.M.1    Tomovski, Z.2
  • 32
    • 77953460296 scopus 로고    scopus 로고
    • A new generalization of the Bernoulli and related polynomials
    • H.M. Srivastava, M. Garg, and S. Choudhary, A new generalization of the Bernoulli and related polynomials, Russian J. Math. Phys. 17 (2010), pp. 251-261.
    • (2010) Russian J. Math. Phys , vol.17 , pp. 251-261
    • Srivastava, H.M.1    Garg, M.2    Choudhary, S.3
  • 34
    • 33845355798 scopus 로고    scopus 로고
    • Some fractional-calculus results for the H-function associated with a class of Feynman integrals
    • H.M. Srivastava, S.-D. Lin, and P.-Y. Wang, Some fractional-calculus results for the H-function associated with a class of Feynman integrals, Russian J. Math. Phys. 13 (2006), pp. 94-100.
    • (2006) Russian J. Math. Phys , vol.13 , pp. 94-100
    • Srivastava, H.M.1    Lin, S.-D.2    Wang, P.-Y.3
  • 36
    • 3042716395 scopus 로고    scopus 로고
    • An integral form for a generalized Zeta function
    • C-E. Yen, M.-L. Lin, and K. Nishimoto, An integral form for a generalized Zeta function, J. Fract. Calc. 22 (2002), pp. 99-102.
    • (2002) J. Fract. Calc , vol.22 , pp. 99-102
    • Yen, C.-E.1    Lin, M.-L.2    Nishimoto, K.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.