Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, , 19 - 27, 25.03.2020
https://doi.org/10.32323/ujma.622495

Öz

Kaynakça

  • [1] W.W. Bell, Special Functions for Scientists and Engineers, Oxford University press, London, 1968.
  • [2] M.G. Bin-Saad, J.A. Younis, Operational representations and generating functions of certain quadruple hypergeometric series, Balkan J. Appl. Math. Info., 1 (2018), 23-28.
  • [3] M.G. Bin-Saad, J.A. Younis, Certain generating functions of some quadruple hypergeometric series, Eurasian Bulletin Math., 2 (2019), 56-62.
  • [4] M.G. Bin-Saad, J.A. Younis, R. Aktas, Integral representations for certain quadruple hypergeometric series, Far East J. Math. Sci., 103 (2018), 21-44.
  • [5] M.G. Bin-Saad, J.A. Younis, R. Aktas, New quadruple hypergeometric series and their integral representations, Sarajevo Math. J., 14 (2018), 45-57.
  • [6] B.C. Carlson, Lauricella´s hypergeometric function FD , J. Math. Anal. Appl., 7 (1963), 452-470.
  • [7] C.A. Downing, M.E. Portnoi, Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields, (2016), doi.org/10.1103/PhysRevB.94.165407.
  • [8] A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
  • [9] H. Exton, Multiple Hypergeometric Functions and Applications, Halsted Press, New York, London, Sydney and Toronto, 1976.
  • [10] H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math., 4 (1982), 113-119.
  • [11] A. Hasanov, H.M. Srivastava, M. Turaev, Decomposition formulas for some triple hypergeometric function, J. Math. Anal. Apple., 324 (2006), 955- 969.
  • [12] G. Lauricella, Sull funzioni ipergeometric a pi variabili, Rend. Cric. Mat. Palermo., 7 (1893), 111-158.
  • [13] N.N. Lebedev, Special Functions and Their Applications, Prentice-Hall, INC, printed in USA, 1965.
  • [14] L. Minjie, R.K. Raina, Extended generalized hypergeometric functions and their applications, Bulletin Math. Anal. Appl., 5 (2013), 65-77.
  • [15] F.W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010.
  • [16] C. Sharma, C.L. Parihar, Hypergeometric functions of four variables (I), J. Indian Acad. Math., 11 (1989), 121-133.
  • [17] S.Yu. Slavyanov, W. Lay, Special Functions, Oxford University Press, Oxford, 2000.
  • [18] H.M. Srivastava, J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
  • [19] H.M. Srivastava, P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Lt1., Chichester, 1984.
  • [20] H.M. Srivastava, H.L. Manocha, A Treatise on Generating Functions, Halsted Press, Bristone, London, New York and Toronto, 1985.
  • [21] Q. Xie, H. Zhong, M.T. Batchelor, C. Lee, The quantum Rabi model: solution and dynamics, J. Phys., (2017), arXiv:1609.00434 [quant-ph].
  • [22] J.A. Younis, Maged G. Bin-Saad, Integral representations and operational relations involving some quadruple hypergeometric functions, J. Frac. Calc. Appl., 11 (2020), 62-74.

Some Integrals Connected with a New Quadruple Hypergeometric Series

Yıl 2020, , 19 - 27, 25.03.2020
https://doi.org/10.32323/ujma.622495

Öz

Hypergeometric function of four variables was introduced by Bin-Saad and Younis. In the present paper a new integral representations of of Euler-type and Laplace-type involving double and triple hypergeometric series for these functions are derived.

Kaynakça

  • [1] W.W. Bell, Special Functions for Scientists and Engineers, Oxford University press, London, 1968.
  • [2] M.G. Bin-Saad, J.A. Younis, Operational representations and generating functions of certain quadruple hypergeometric series, Balkan J. Appl. Math. Info., 1 (2018), 23-28.
  • [3] M.G. Bin-Saad, J.A. Younis, Certain generating functions of some quadruple hypergeometric series, Eurasian Bulletin Math., 2 (2019), 56-62.
  • [4] M.G. Bin-Saad, J.A. Younis, R. Aktas, Integral representations for certain quadruple hypergeometric series, Far East J. Math. Sci., 103 (2018), 21-44.
  • [5] M.G. Bin-Saad, J.A. Younis, R. Aktas, New quadruple hypergeometric series and their integral representations, Sarajevo Math. J., 14 (2018), 45-57.
  • [6] B.C. Carlson, Lauricella´s hypergeometric function FD , J. Math. Anal. Appl., 7 (1963), 452-470.
  • [7] C.A. Downing, M.E. Portnoi, Massless Dirac fermions in two dimensions: Confinement in nonuniform magnetic fields, (2016), doi.org/10.1103/PhysRevB.94.165407.
  • [8] A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill Book Company, New York, Toronto and London, 1953.
  • [9] H. Exton, Multiple Hypergeometric Functions and Applications, Halsted Press, New York, London, Sydney and Toronto, 1976.
  • [10] H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math., 4 (1982), 113-119.
  • [11] A. Hasanov, H.M. Srivastava, M. Turaev, Decomposition formulas for some triple hypergeometric function, J. Math. Anal. Apple., 324 (2006), 955- 969.
  • [12] G. Lauricella, Sull funzioni ipergeometric a pi variabili, Rend. Cric. Mat. Palermo., 7 (1893), 111-158.
  • [13] N.N. Lebedev, Special Functions and Their Applications, Prentice-Hall, INC, printed in USA, 1965.
  • [14] L. Minjie, R.K. Raina, Extended generalized hypergeometric functions and their applications, Bulletin Math. Anal. Appl., 5 (2013), 65-77.
  • [15] F.W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010.
  • [16] C. Sharma, C.L. Parihar, Hypergeometric functions of four variables (I), J. Indian Acad. Math., 11 (1989), 121-133.
  • [17] S.Yu. Slavyanov, W. Lay, Special Functions, Oxford University Press, Oxford, 2000.
  • [18] H.M. Srivastava, J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
  • [19] H.M. Srivastava, P.W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Horwood Lt1., Chichester, 1984.
  • [20] H.M. Srivastava, H.L. Manocha, A Treatise on Generating Functions, Halsted Press, Bristone, London, New York and Toronto, 1985.
  • [21] Q. Xie, H. Zhong, M.T. Batchelor, C. Lee, The quantum Rabi model: solution and dynamics, J. Phys., (2017), arXiv:1609.00434 [quant-ph].
  • [22] J.A. Younis, Maged G. Bin-Saad, Integral representations and operational relations involving some quadruple hypergeometric functions, J. Frac. Calc. Appl., 11 (2020), 62-74.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Jihad Younis 0000-0001-7116-3251

Maged Bin-saad

Yayımlanma Tarihi 25 Mart 2020
Gönderilme Tarihi 20 Eylül 2019
Kabul Tarihi 30 Aralık 2019
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Younis, J., & Bin-saad, M. (2020). Some Integrals Connected with a New Quadruple Hypergeometric Series. Universal Journal of Mathematics and Applications, 3(1), 19-27. https://doi.org/10.32323/ujma.622495
AMA Younis J, Bin-saad M. Some Integrals Connected with a New Quadruple Hypergeometric Series. Univ. J. Math. Appl. Mart 2020;3(1):19-27. doi:10.32323/ujma.622495
Chicago Younis, Jihad, ve Maged Bin-saad. “Some Integrals Connected With a New Quadruple Hypergeometric Series”. Universal Journal of Mathematics and Applications 3, sy. 1 (Mart 2020): 19-27. https://doi.org/10.32323/ujma.622495.
EndNote Younis J, Bin-saad M (01 Mart 2020) Some Integrals Connected with a New Quadruple Hypergeometric Series. Universal Journal of Mathematics and Applications 3 1 19–27.
IEEE J. Younis ve M. Bin-saad, “Some Integrals Connected with a New Quadruple Hypergeometric Series”, Univ. J. Math. Appl., c. 3, sy. 1, ss. 19–27, 2020, doi: 10.32323/ujma.622495.
ISNAD Younis, Jihad - Bin-saad, Maged. “Some Integrals Connected With a New Quadruple Hypergeometric Series”. Universal Journal of Mathematics and Applications 3/1 (Mart 2020), 19-27. https://doi.org/10.32323/ujma.622495.
JAMA Younis J, Bin-saad M. Some Integrals Connected with a New Quadruple Hypergeometric Series. Univ. J. Math. Appl. 2020;3:19–27.
MLA Younis, Jihad ve Maged Bin-saad. “Some Integrals Connected With a New Quadruple Hypergeometric Series”. Universal Journal of Mathematics and Applications, c. 3, sy. 1, 2020, ss. 19-27, doi:10.32323/ujma.622495.
Vancouver Younis J, Bin-saad M. Some Integrals Connected with a New Quadruple Hypergeometric Series. Univ. J. Math. Appl. 2020;3(1):19-27.

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