메뉴 건너뛰기




Volumn 2, Issue 1, 2013, Pages 1-23

Generating relations and other results associated with some families of the extended Hurwitz-Lerch Zeta functions

Author keywords

Fox Wright 9 function and the H function; Gauss and Kummer hypergeometric functions; General Hurwitz Lerch Zeta function; Generating functions and Eulerian Gamma function and Beta function integral representations; Hurwitz (or generalized) and Hurwitz Lerch Zeta functions; Lerch Zeta function and the Polylogarithmic (or de Jonqui re's) function; Mellin Barnes type integral representations and Meromorphic continuation; Mittag Leffler type functions; Riemann

Indexed keywords


EID: 84876554013     PISSN: None     EISSN: 21931801     Source Type: Journal    
DOI: 10.1186/2193-1801-2-67     Document Type: Article
Times cited : (31)

References (45)
  • 1
    • 0347084839 scopus 로고    scopus 로고
    • On a generalized gamma-type distribution with τ-confluent hypergeometric function
    • Al-Zamel A (2001) On a generalized gamma-type distribution with τ-confluent hypergeometric function. Kuwait J Sci Engrg 28:25-36
    • (2001) Kuwait J Sci Engrg , vol.28 , pp. 25-36
    • Al-Zamel, A.1
  • 2
    • 0042793291 scopus 로고    scopus 로고
    • A generalized inverse Gaussian distribution with τ-confluent hypergeometric function
    • Ali I, Kalla SL, Khajah HG (2001) A generalized inverse Gaussian distribution with τ-confluent hypergeometric function. Integral Transforms Spec Funct 12:101-114
    • (2001) Integral Transforms Spec Funct , vol.12 , pp. 101-114
    • Ali, I.1    Kalla, S.L.2    Khajah, H.G.3
  • 3
    • 70349526348 scopus 로고    scopus 로고
    • Sums and partial sums of double power series associated with the generalized Zeta function and their N-Fractional calculus
    • Bin-Saad MG (2007) Sums and partial sums of double power series associated with the generalized Zeta function and their N-Fractional calculus. Math J Okayama Univ 49:37-52
    • (2007) Math J Okayama Univ , vol.49 , pp. 37-52
    • Bin-Saad, M.G.1
  • 4
    • 33845368302 scopus 로고
    • The H-function associated with a certain class of Feynman integrals
    • Buschman RG, Srivastava HM (1990) The H-function associated with a certain class of Feynman integrals. J Phys A: Math Gen 23:4707-4710
    • (1990) J Phys A: Math Gen , vol.23 , pp. 4707-4710
    • Buschman, R.G.1    Srivastava, H.M.2
  • 8
    • 79955464613 scopus 로고    scopus 로고
    • A further study of general Hurwitz-Lerch Zeta function
    • Garg M, Jain K, Kalla SL (2008) A further study of general Hurwitz-Lerch Zeta function. Algebras Groups Geom. 25:311-319
    • (2008) Algebras Groups Geom. , vol.25 , 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
    • Garg M, Jain K, Srivastava HM (2006) Some relationships between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta functions. Integral Transforms Spec Funct 17:803-815
    • (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
    • Goyal SP, Laddha RK (1997) On the generalized Zeta function and the generalized Lambert function. Gȧnita Sandesh 11:99-108
    • (1997) Gȧnita Sandesh , vol.11 , pp. 99-108
    • Goyal, S.P.1    Laddha, R.K.2
  • 11
    • 84876522415 scopus 로고    scopus 로고
    • Some results on a τ-generalized Riemann Zeta function
    • Gupta RK, Kumari M (2011) Some results on a τ-generalized Riemann Zeta function. Jñ-an-abha 41:63-68
    • (2011) Jñ-an-abha , vol.41 , pp. 63-68
    • Gupta, R.K.1    Kumari, M.2
  • 12
    • 38649091739 scopus 로고    scopus 로고
    • A class of Hurwitz-Lerch Zeta distributions and their applications in reliability
    • Gupta PL, Gupta RC, Ong S-H, Srivastava HM (2008) A class of Hurwitz-Lerch Zeta distributions and their applications in reliability. Appl Math Comput 196:521-531
    • (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
  • 13
    • 0007270304 scopus 로고
    • New properties of hypergeometric series derivable from Feynman integrals. I: Transformation and reduction formulae
    • Inayat-Hussain AA (1987a) New properties of hypergeometric series derivable from Feynman integrals. I: Transformation and reduction formulae. J Phys A: Math Gen 20:4109-4117
    • (1987) J Phys A: Math Gen , vol.20 , pp. 4109-4117
    • Inayat-Hussain, A.A.1
  • 14
    • 33845372007 scopus 로고
    • New properties of hypergeometric series derivable from Feynman integrals. II: A generalization of the H-function
    • Inayat-Hussain AA (1987b) New properties of hypergeometric series derivable from Feynman integrals. II: A generalization of the H-function. J Phys A: Math Gen 20:4119-4128
    • (1987) J Phys A: Math Gen , vol.20 , pp. 4119-4128
    • Inayat-Hussain, A.A.1
  • 15
    • 79955474305 scopus 로고    scopus 로고
    • An extended general Hurwitz-Lerch Zeta function as a Mathieu (a, λ)-series
    • Jankov D, Pogány TK, Saxena RK (2011) An extended general Hurwitz-Lerch Zeta function as a Mathieu (a, λ)-series. Appl Math Lett 24:1473-1476
    • (2011) Appl Math Lett , vol.24 , pp. 1473-1476
    • Jankov, D.1    Pogány, T.K.2    Saxena, R.K.3
  • 16
    • 0007191331 scopus 로고    scopus 로고
    • On Mellin-Barnes type of integrals and sums associated with the Riemann Zetafunction
    • Katsurada M (1997) On Mellin-Barnes type of integrals and sums associated with the Riemann Zetafunction. Publ Inst Math (Beograd) (Nouvelle Ser) 62(76):13-25
    • (1997) Publ Inst Math (Beograd) (Nouvelle Ser) , vol.62 , Issue.76 , pp. 13-25
    • Katsurada, M.1
  • 19
    • 3042752343 scopus 로고    scopus 로고
    • Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations
    • Lin S-D, Srivastava HM (2004) Some families of the Hurwitz-Lerch Zeta functions and associated fractional derivative and other integral representations. Appl Math Comput 154:725-733
    • (2004) Appl Math Comput , vol.154 , pp. 725-733
    • Lin, S.-D.1    Srivastava, H.M.2
  • 20
    • 33749664753 scopus 로고    scopus 로고
    • Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions
    • Lin S-D, Srivastava HM, Wang P-Y (2006) Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions. Integral Transforms Spec Funct 17:817-827
    • (2006) Integral Transforms Spec Funct , vol.17 , pp. 817-827
    • Lin, S.-D.1    Srivastava, H.M.2    Wang, P.-Y.3
  • 22
    • 3042829374 scopus 로고    scopus 로고
    • Some integral forms for a generalized Zeta function
    • Nishimoto K, Yen C-E, Lin M-L (2002) Some integral forms for a generalized Zeta function. J Fract Calc 22:91-97
    • (2002) J Fract Calc , vol.22 , pp. 91-97
    • Nishimoto, K.1    Yen, C.-E.2    Lin, M.-L.3
  • 23
    • 36949010134 scopus 로고    scopus 로고
    • A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch Zeta function
    • Řaducanu D, Srivastava HM (2007) A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch Zeta function. Integral Transforms Spec Funct 18:933-943
    • (2007) Integral Transforms Spec Funct , vol.18 , pp. 933-943
    • Řaducanu, D.1    Srivastava, H.M.2
  • 25
    • 80052671107 scopus 로고    scopus 로고
    • A remark on a paper on M-series [MR2401326 (2009b:26008)]. With an editorial note
    • Saxana RK (2009) A remark on a paper on M-series [MR2401326 (2009b:26008)]. With an editorial note. Fract Calc Appl Anal 12:109-110
    • (2009) Fract Calc Appl Anal , vol.12 , pp. 109-110
    • Saxana, R.K.1
  • 26
    • 84876533532 scopus 로고    scopus 로고
    • Integrals and series expansions of the τ-generalized Riemann Zeta function
    • Saxena RK, Gupta RK, KumariM(2011a) Integrals and series expansions of the τ-generalized Riemann Zeta function. J Indian Acad Math 33:309-320
    • (2011) J Indian Acad Math , vol.33 , pp. 309-320
    • Saxena, R.K.1    Gupta, R.K.2    Kumari, M.3
  • 27
    • 84876518548 scopus 로고    scopus 로고
    • On generalized Hurwitz-Lerch Zeta distributions occurring in statistical inference
    • Saxena RK, Pog'any TK, Saxena R, Jankov D (2011b) On generalized Hurwitz-Lerch Zeta distributions occurring in statistical inference. Acta Univ Sapientiae Math 3:43-59
    • (2011) Acta Univ Sapientiae Math , vol.3 , pp. 43-59
    • Saxena, R.K.1    Pog'any, T.K.2    Saxena, R.3    Jankov, D.4
  • 28
    • 79551616683 scopus 로고    scopus 로고
    • Fractional integration and fractional differentiation of the M-series
    • Sharma M (2008) Fractional integration and fractional differentiation of the M-series. Fract Calc Appl Anal 11:187-191
    • (2008) Fract Calc Appl Anal , vol.11 , pp. 187-191
    • Sharma, M.1
  • 29
    • 79251576218 scopus 로고    scopus 로고
    • A note on a generalzed M-series as a special function of fractional calculus
    • Sharma M, Jain R (2009) A note on a generalzed M-series as a special function of fractional calculus. Fract Calc Appl Anal 12:449-452
    • (2009) Fract Calc Appl Anal , vol.12 , pp. 449-452
    • Sharma, M.1    Jain, R.2
  • 30
    • 38249026905 scopus 로고
    • Sums of certain series of the Riemann Zeta function
    • Srivastava HM (1988a) Sums of certain series of the Riemann Zeta function. J Math Anal Appl 134:129-140
    • (1988) J Math Anal Appl , vol.134 , pp. 129-140
    • Srivastava, H.M.1
  • 31
    • 0002676205 scopus 로고
    • A unified presentation of certain classes of series of the Riemann Zeta function
    • Srivastava HM (1988b) A unified presentation of certain classes of series of the Riemann Zeta function. Riv Mat Univ Parma (Ser. 4) 14:1-23
    • (1988) Riv Mat Univ Parma (Ser. 4) , vol.14 , pp. 1-23
    • Srivastava, H.M.1
  • 32
    • 23044520680 scopus 로고    scopus 로고
    • Some formulas for the Bernoulli and Euler polynomials at rational arguments
    • Srivastava HM (2000) Some formulas for the Bernoulli and Euler polynomials at rational arguments. Math Proc Cambridge Philos Soc 129:77-84
    • (2000) Math Proc Cambridge Philos Soc , vol.129 , pp. 77-84
    • Srivastava, H.M.1
  • 33
    • 84857133939 scopus 로고    scopus 로고
    • Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials
    • Srivastava HM (2011) Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials. Appl Math Inform Sci 5:390-444
    • (2011) Appl Math Inform Sci , vol.5 , pp. 390-444
    • Srivastava, H.M.1
  • 36
    • 77953460296 scopus 로고    scopus 로고
    • A new generalization of the Bernoulli and related polynomials
    • Srivastava HM, Garg M, Choudhary S (2010) A new generalization of the Bernoulli and related polynomials, Russian J Math Phys 17:251-261
    • (2010) Russian J Math Phys , vol.17 , pp. 251-261
    • Srivastava, H.M.1    Garg, M.2    Choudhary, S.3
  • 40
    • 33845355798 scopus 로고    scopus 로고
    • Some fractional-calculus results for the H-function associated with a class of Feynman integrals
    • Srivastava HM, Lin S-D, Wang P-Y (2006) Some fractional-calculus results for the H-function associated with a class of Feynman integrals. Russian J Math Phys 13:94-100
    • (2006) Russian J Math Phys , vol.13 , pp. 94-100
    • Srivastava, H.M.1    Lin, S.-D.2    Wang, P.-Y.3
  • 41
    • 0004162942 scopus 로고
    • Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto
    • Srivastava HM, Manocha HL (1984) A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto
    • (1984) A Treatise on Generating Functions
    • Srivastava, H.M.1    Manocha, H.L.2
  • 44
    • 0001847762 scopus 로고
    • A proof of Burnside's formula for log Γ(x + 1) and certain allied properties of Riemann's ζ-function
    • Wilton JR (1922/1923) A proof of Burnside's formula for log Γ(x + 1) and certain allied properties of Riemann's ζ-function. Messenger Math 52:90-93.
    • (1922) Messenger Math , vol.52 , pp. 90-93
    • Wilton, J.R.1
  • 45
    • 3042716395 scopus 로고    scopus 로고
    • An integral form for a generalized Zeta function
    • Yen C-E, Lin M-L, Nishimoto K (2002) An integral form for a generalized Zeta function. J Fract Calc 23:99-102
    • (2002) J Fract Calc , vol.23 , pp. 99-102
    • Yen, C.-E.1    Lin, M.-L.2    Nishimoto, K.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.