메뉴 건너뛰기




Volumn 8, Issue 4, 2014, Pages 1485-1500

A new family of the λ-generalized hurwitz-lerch zeta functions with applications

Author keywords

Generalized hurwitz lerch zeta functions; Analytic number theory; Derivative properties; Generalized hurwitz meausure; Hurwitz Lerch zeta function; Mellin Barnes contour integral representations; Partial differential equations; Probability density functions; Series representations

Indexed keywords


EID: 84894105344     PISSN: 19350090     EISSN: 23250399     Source Type: Journal    
DOI: 10.12785/amis/080402     Document Type: Article
Times cited : (68)

References (36)
  • 1
    • 0003851729 scopus 로고
    • (Editors),:, rApplied Mathematics Series, National Bureau of Standards, Washington, D.C., Reprinted by Dover Publications, New York, (1965) (see also [22])
    • M. Abramowitz and I. A. Stegun (Editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series, National Bureau of Standards, Washington, D.C., 55, 1964; Reprinted by Dover Publications, New York, (1965) (see also [22]).
    • (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , vol.55
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 84893713758 scopus 로고    scopus 로고
    • Reduction and duality of the generalized Hurwitz-Lerch zetas
    • Article ID 82
    • A. Bayad and J. Chikhi, Reduction and duality of the generalized Hurwitz-Lerch zetas, Fixed Point Theory Appl., 2013, Article ID 82, 1-14 (2013).
    • (2013) Fixed Point Theory Appl. , vol.2013 , pp. 1-14
    • Bayad, A.1    Chikhi, J.2
  • 3
    • 84887971955 scopus 로고    scopus 로고
    • Generalized Dirichlet L-function of arbitrary order with applications
    • A. Bayad and S. Gaboury, Generalized Dirichlet L-function of arbitrary order with applications, Adv. Stud. Contemp. Math., 23, 607-619 (2013).
    • (2013) Adv. Stud. Contemp. Math. , vol.23 , pp. 607-619
    • Bayad, A.1    Gaboury, S.2
  • 7
    • 84893715479 scopus 로고    scopus 로고
    • Series representations at special values of generalized Hurwitz-Lerch zeta function
    • Article ID 975615
    • S. Gaboury and A. Bayad, Series representations at special values of generalized Hurwitz-Lerch zeta function, Abstr. Appl. Anal., 2013, Article ID 975615, 1-8 (2013).
    • (2013) Abstr. Appl. Anal. , vol.2013 , pp. 1-8
    • Gaboury, S.1    Bayad, A.2
  • 8
    • 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), 311-319 (2008).
    • (2008) Algebras Groups Geom. , vol.25 , Issue.2008 , pp. 311-319
    • Garg, M.1    Jain, K.2    Kalla, S.L.3
  • 9
    • 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), 803-815.
    • (2006) Integral Transforms Spec. Funct. , vol.17 , pp. 803-815
    • Garg, M.1    Jain, K.2    Srivastava, H.M.3
  • 10
    • 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, Gaṅita Sandesh, 11, 99-108 (1997).
    • (1997) Gaṅita Sandesh , vol.11 , pp. 99-108
    • Goyal, S.P.1    Laddha, R.K.2
  • 11
    • 49849109565 scopus 로고
    • A class of probability distributions on the integers
    • S. W. Golomb, A class of probability distributions on the integers, J. Number Theory, 2, 189-192 (1970).
    • (1970) J. Number Theory , vol.2 , pp. 189-192
    • Golomb, S.W.1
  • 12
    • 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, 521-531 (2008).
    • (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
  • 13
    • 79955811417 scopus 로고    scopus 로고
    • Chapman and Hall (CRC Press Company), Boca Raton, London, New York and Washington, D.C.
    • A. A. Kilbas and M. Saigo, H-Transforms: Theory and Applications, Chapman and Hall (CRC Press Company), Boca Raton, London, New York and Washington, D.C., (2004).
    • (2004) H-Transforms: Theory and Applications
    • Kilbas, A.A.1    Saigo, M.2
  • 15
    • 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, 725-733 (2004).
    • (2004) Appl. Math. Comput. , vol.154 , pp. 725-733
    • Lin, S.-D.1    Srivastava, H.M.2
  • 16
    • 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, 817-827 (2006).
    • (2006) Integral Transforms Spec. Funct. , vol.17 , pp. 817-827
    • Lin, S.-D.1    Srivastava, H.M.2    Wang, P.-Y.3
  • 17
    • 38249007186 scopus 로고
    • A probabilistic interpretation of the Hurwitz zeta function
    • R. A. Lippert, A probabilistic interpretation of the Hurwitz zeta function, Adv. Math., 97, 278-284 (1993).
    • (1993) Adv. Math. , vol.97 , pp. 278-284
    • Lippert, R.A.1
  • 18
    • 84894025064 scopus 로고    scopus 로고
    • Some new results related to a class of generalized Hurwitz zeta function
    • Preprint, (submitted for publication)
    • M.-J. Luo and R. K. Raina, Some new results related to a class of generalized Hurwitz zeta function, Preprint 2013 [Ann. Polon. Math. (submitted for publication)].
    • (2013) Ann. Polon. Math
    • Luo, M.-J.1    Raina, R.K.2
  • 22
    • 77954499023 scopus 로고    scopus 로고
    • (Editors),:, [With 1 CD-ROM (Windows, Macintosh and UNIX)], U. S. Department of Commerce, National Institute of Standards and Technology, Washington, D. C., (2010); Cambridge University Press, Cambridge, London and New York, (see also [1])
    • F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark (Editors), NIST Handbook of Mathematical Functions [With 1 CD-ROM (Windows, Macintosh and UNIX)], U. S. Department of Commerce, National Institute of Standards and Technology, Washington, D. C., (2010); Cambridge University Press, Cambridge, London and New York, (2010) (see also [1]).
    • (2010) NIST Handbook of Mathematical Functions
    • Olver, F.W.J.1    Lozier, D.W.2    Boisvert, R.F.3    Clark, C.W.4
  • 23
    • 4043057192 scopus 로고    scopus 로고
    • Certain results involving a class of functions associated with the Hurwitz zeta function
    • R. K. Raina and P. K. Chhajed, Certain results involving a class of functions associated with the Hurwitz zeta function, Acta Math. Univ. Comenianae, 73, 89-100 (2004).
    • (2004) Acta Math. Univ. Comenianae , vol.73 , pp. 89-100
    • Raina, R.K.1    Chhajed, P.K.2
  • 25
    • 84876518548 scopus 로고    scopus 로고
    • On generalized Hurwitz-Lerch Zeta distributions occurring in statistical inference
    • R. K. Saxena, T. K. Pogány, R. Saxena and D. Jankov, On generalized Hurwitz-Lerch Zeta distributions occurring in statistical inference, Acta Univ. Sapientiae Math., 3, 43-59 (2011).
    • (2011) Acta Univ. Sapientiae Math. , vol.3 , pp. 43-59
    • Saxena, R.K.1    Pogány, T.K.2    Saxena, R.3    Jankov, D.4
  • 26
    • 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, 77-84 (2000).
    • (2000) Math. Proc. Cambridge Philos. Soc. , vol.129 , pp. 77-84
    • Srivastava, H.M.1
  • 27
    • 84857133939 scopus 로고    scopus 로고
    • Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials
    • H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inform. Sci., 5, 390-444 (2011).
    • (2011) Appl. Math. Inform. Sci. , vol.5 , pp. 390-444
    • Srivastava, H.M.1
  • 28
    • 84876554013 scopus 로고    scopus 로고
    • Generating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions
    • Article ID 2
    • H. M. Srivastava, Generating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions, SpringerPlus, 2, Article ID 2:67, 1-14 (2013).
    • (2013) SpringerPlus 2 , vol.67 , pp. 1-14
    • Srivastava, H.M.1
  • 32
    • 79959521359 scopus 로고    scopus 로고
    • Two-sided inequalities for the extended Hurwitz-Lerch Zeta function
    • H.M. Srivastava, D. Jankov, T. K. Pogány and R. K. Saxena, Two-sided inequalities for the extended Hurwitz-Lerch Zeta function, Comput. Math. Appl., 62, 516-522 (2011).
    • (2011) Comput. Math. Appl. , vol.62 , pp. 516-522
    • Srivastava, H.M.1    Jankov, D.2    Pogány, T.K.3    Saxena, R.K.4
  • 33
    • 0003791753 scopus 로고
    • Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto
    • H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1985).
    • (1985) Multiple Gaussian Hypergeometric Series
    • Srivastava, H.M.1    Karlsson, P.W.2
  • 34
    • 84894106092 scopus 로고    scopus 로고
    • New results involving a class of generalized Hurwitz-Lerch zeta functions and their applications
    • H. M. Srivastava, M.-J. Luo and R. K. Raina, New results involving a class of generalized Hurwitz-Lerch zeta functions and their applications, Turkish J. Anal. Number Theory, 1, 26-35 (2013).
    • (2013) Turkish J. Anal. Number Theory , vol.1 , pp. 26-35
    • Srivastava, H.M.1    Luo, M.-J.2    Raina, R.K.3
  • 35
    • 0004162942 scopus 로고
    • Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto
    • H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, (1984).
    • (1984) A Treatise on Generating Functions
    • Srivastava, H.M.1    Manocha, H.L.2
  • 36
    • 79959327160 scopus 로고    scopus 로고
    • Integral and computational representations of the extended Hurwitz-Lerch Zeta function
    • H. M. Srivastava, R. K. Saxena, T. K. Pogány and R. Saxena, Integral and computational representations of the extended Hurwitz-Lerch Zeta function, Integral Transforms Spec. Funct., 22, 487-506 (2011).
    • (2011) Integral Transforms Spec. Funct. , vol.22 , pp. 487-506
    • Srivastava, H.M.1    Saxena, R.K.2    Pogány, T.K.3    Saxena, R.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.