Research Article
BibTex RIS Cite

A New Type Multivariable Multiple Hypergeometric Functions

Year 2021, , 359 - 372, 31.12.2021
https://doi.org/10.47000/tjmcs.954676

Abstract

We define a new type of multivariable multiple hypergeometric functions in this paper, which is inspired by Exton's multiple hypergeometric functions given by in [13]. Then, for these functions, we obtain some certain type linear generating functions. After that, we derive a variety classes of multilinear and multilateral generating functions for a family of the multivariable multiple hypergeometric functions. In addition, by employing the Erkus-Srivastava polynomials (see [11]) and the fourth type multivariable Horn functions (see [13]), we have also provided some of its conclusions.

Supporting Institution

No

Project Number

No

References

  • [1] Abreu, S., Britto, R., Duhr, C., Gardi, E., Matthew, J., From positive geometries to a coaction on hypergeometric functions, Journal of High Energy Physics, 2(2020), 1–45.
  • [2] Agarwal, R.P., Luo, M.J., Agarwal, P., On the extended Appell Lauricella hypergeometric functions and their applications, Filomat, 31(2017), 3693–3713.
  • [3] Altin, A., Cekim, B., Sahin, R., On the matrix versions of Appell hypergeometric functions, Quaestiones Mathematicae, 37(2014), 31–38.
  • [4] Bezrodnykh, S.I., Analytic continuation of Lauricella’s functions, FA(N), FB(N) and FD(N), Integral Transforms and Special Functions, 31(2020), 921–940.
  • [5] Bezrodnykh, S.I., Horn’s hypergeometric functions with three variables, Integral Transforms and Special Functions, 32(2021), 207–223.
  • [6] Brychkov, Y.A., Saad, N., On some formulas for the Appell function F 2 (a, b, b’; c, c’; w; z), Integral Transforms and Special Functions, 25(2014), 111–123.
  • [7] Brychkov, Y.A., Savischenko, N.V., On some formulas for the Horn functions H 4 (a, b; c, c’; w, z) and H 7 (c)(a; c, c’; w, z), Integral Transforms and Special Functions, 32(2021), 1–19.
  • [8] Choi, J., A generalization of Gottlieb polynomials in several variables, Applied Mathematics Letters, 25(2012), 43–46.
  • [9] Dwivedi, R., Sahai, V., A note on the Appell matrix functions, Quaestiones Mathematicae, 43(2020), 321–334.
  • [10] Ergashev, T.G., Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables, Lobachevskii Journal of Mathematics, 41(2020), 15–26.
  • [11] Erkuş, E., Srivastava, H.M., A unified presentation of some families of multivariable polynomials, Integral Transform. Spec. Funct., 17(2006), 267–273.
  • [12] Ernst, T., Some results for q functions of many variables, Rendiconti del Seminario Matematico della Universit´a di Padova, 112(2004), 199-235.
  • [13] Exton, H., Multiple Hypergeometric Functions and Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1976.
  • [14] Gürel Yılmaz, Ö., Aktaş, R., Taşdelen, F., On some formulas for the k-analogue of Appell functions and generating relations via k-fractional derivative, Fractal and Fractional, 4(2020), 48.
  • [15] Hidan, M., Abdalla, M., A note on the Appell hypergeometric matrix function F2, Mathematical Problems in Engineering, (2020).
  • [16] Horn, J., Hypergeometrische funktionen zweier Ver¨anderlichen, Math. Ann., 105(1931), 381–407.
  • [17] Jaeger, J.C., Hulme, H.R., The internal conversion of Gamma rays with the production of electrons and positrons, Proceedings of the Royal Society of London A, 148(1935), 708–728.
  • [18] Kalla, S.L., Parmar, R.K., Purohit, S.D., Some extensions of Lauricella Functions of sevearal variables, Communications of the Korean Mathematical Society, 30(2015), 239–252.
  • [19] Korkmaz Duzgun, D., Erkus Duman, E., Extended multivariable fourth type Horn functions, Gazi University Journal of Science, 32(2019), 225–240.
  • [20] Korkmaz Duzgun, D., Erkuş Duman, E., Generating functions for the extended multivariable fourth type Horn functions, International Journal of Applied Physics and Mathematics, 10(2020), 65–72.
  • [21] Lauricella, G., Sulle funzioni ipergeometriche a piu variabili, Rendiconti del Circolo Matematico di Palermo, 7(1983), 111–158.
  • [22] Liu, S.J., Chyan, C.J., Lu, H.C., Srivastava, H.M., Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella functions, Integral Transforms and Special Functions, 23(2012), 539–549.
  • [23] Ma, H., Some properties for Appell series F2 over finite fields, Integral Transforms and Special Functions, 30(2019), 992–1003.
  • [24] Olsson P.O.M., A hypergeometric function of two variables of importance in perturbation theory I and II, Arkiv för Fysik; 30(1965), 187–191, ibid. 29(1965), 459–465.
  • [25] Ozmen, N., Erkuş Duman, E., Some generating functions for a class of hypergeometric polynomials, Gazi University Journal of Science, 31(2018), 1179–1190.
  • [26] Özmen, N., Some new properties of generalized Bessel polynomials, Applicationes Mathematicae, 46(2019), 85–98.
  • [27] Rainville, E.D., Special Functions, The Macmillan Company, New York, 1960.
  • [28] Scarpello, G.M., Ritelli, D., On computing some special values of multivariate hypergeometric functions, Journal of Mathematical Analysis and Applications, 420(2014), 1693–1718.
  • [29] Srivastava, H.M., Manocha, H.L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
  • [30] Upadhyaya, L.M., Remarks on Horn’s double hypergeometric functions of matrix arguments, Bulletin of Pure and Applied Sciences-Mathematics, 1(2011), 11–18.
Year 2021, , 359 - 372, 31.12.2021
https://doi.org/10.47000/tjmcs.954676

Abstract

Project Number

No

References

  • [1] Abreu, S., Britto, R., Duhr, C., Gardi, E., Matthew, J., From positive geometries to a coaction on hypergeometric functions, Journal of High Energy Physics, 2(2020), 1–45.
  • [2] Agarwal, R.P., Luo, M.J., Agarwal, P., On the extended Appell Lauricella hypergeometric functions and their applications, Filomat, 31(2017), 3693–3713.
  • [3] Altin, A., Cekim, B., Sahin, R., On the matrix versions of Appell hypergeometric functions, Quaestiones Mathematicae, 37(2014), 31–38.
  • [4] Bezrodnykh, S.I., Analytic continuation of Lauricella’s functions, FA(N), FB(N) and FD(N), Integral Transforms and Special Functions, 31(2020), 921–940.
  • [5] Bezrodnykh, S.I., Horn’s hypergeometric functions with three variables, Integral Transforms and Special Functions, 32(2021), 207–223.
  • [6] Brychkov, Y.A., Saad, N., On some formulas for the Appell function F 2 (a, b, b’; c, c’; w; z), Integral Transforms and Special Functions, 25(2014), 111–123.
  • [7] Brychkov, Y.A., Savischenko, N.V., On some formulas for the Horn functions H 4 (a, b; c, c’; w, z) and H 7 (c)(a; c, c’; w, z), Integral Transforms and Special Functions, 32(2021), 1–19.
  • [8] Choi, J., A generalization of Gottlieb polynomials in several variables, Applied Mathematics Letters, 25(2012), 43–46.
  • [9] Dwivedi, R., Sahai, V., A note on the Appell matrix functions, Quaestiones Mathematicae, 43(2020), 321–334.
  • [10] Ergashev, T.G., Fundamental solutions of the generalized Helmholtz equation with several singular coefficients and confluent hypergeometric functions of many variables, Lobachevskii Journal of Mathematics, 41(2020), 15–26.
  • [11] Erkuş, E., Srivastava, H.M., A unified presentation of some families of multivariable polynomials, Integral Transform. Spec. Funct., 17(2006), 267–273.
  • [12] Ernst, T., Some results for q functions of many variables, Rendiconti del Seminario Matematico della Universit´a di Padova, 112(2004), 199-235.
  • [13] Exton, H., Multiple Hypergeometric Functions and Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1976.
  • [14] Gürel Yılmaz, Ö., Aktaş, R., Taşdelen, F., On some formulas for the k-analogue of Appell functions and generating relations via k-fractional derivative, Fractal and Fractional, 4(2020), 48.
  • [15] Hidan, M., Abdalla, M., A note on the Appell hypergeometric matrix function F2, Mathematical Problems in Engineering, (2020).
  • [16] Horn, J., Hypergeometrische funktionen zweier Ver¨anderlichen, Math. Ann., 105(1931), 381–407.
  • [17] Jaeger, J.C., Hulme, H.R., The internal conversion of Gamma rays with the production of electrons and positrons, Proceedings of the Royal Society of London A, 148(1935), 708–728.
  • [18] Kalla, S.L., Parmar, R.K., Purohit, S.D., Some extensions of Lauricella Functions of sevearal variables, Communications of the Korean Mathematical Society, 30(2015), 239–252.
  • [19] Korkmaz Duzgun, D., Erkus Duman, E., Extended multivariable fourth type Horn functions, Gazi University Journal of Science, 32(2019), 225–240.
  • [20] Korkmaz Duzgun, D., Erkuş Duman, E., Generating functions for the extended multivariable fourth type Horn functions, International Journal of Applied Physics and Mathematics, 10(2020), 65–72.
  • [21] Lauricella, G., Sulle funzioni ipergeometriche a piu variabili, Rendiconti del Circolo Matematico di Palermo, 7(1983), 111–158.
  • [22] Liu, S.J., Chyan, C.J., Lu, H.C., Srivastava, H.M., Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella functions, Integral Transforms and Special Functions, 23(2012), 539–549.
  • [23] Ma, H., Some properties for Appell series F2 over finite fields, Integral Transforms and Special Functions, 30(2019), 992–1003.
  • [24] Olsson P.O.M., A hypergeometric function of two variables of importance in perturbation theory I and II, Arkiv för Fysik; 30(1965), 187–191, ibid. 29(1965), 459–465.
  • [25] Ozmen, N., Erkuş Duman, E., Some generating functions for a class of hypergeometric polynomials, Gazi University Journal of Science, 31(2018), 1179–1190.
  • [26] Özmen, N., Some new properties of generalized Bessel polynomials, Applicationes Mathematicae, 46(2019), 85–98.
  • [27] Rainville, E.D., Special Functions, The Macmillan Company, New York, 1960.
  • [28] Scarpello, G.M., Ritelli, D., On computing some special values of multivariate hypergeometric functions, Journal of Mathematical Analysis and Applications, 420(2014), 1693–1718.
  • [29] Srivastava, H.M., Manocha, H.L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
  • [30] Upadhyaya, L.M., Remarks on Horn’s double hypergeometric functions of matrix arguments, Bulletin of Pure and Applied Sciences-Mathematics, 1(2011), 11–18.
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Duriye Korkmaz-duzgun 0000-0002-2585-987X

Project Number No
Publication Date December 31, 2021
Published in Issue Year 2021

Cite

APA Korkmaz-duzgun, D. (2021). A New Type Multivariable Multiple Hypergeometric Functions. Turkish Journal of Mathematics and Computer Science, 13(2), 359-372. https://doi.org/10.47000/tjmcs.954676
AMA Korkmaz-duzgun D. A New Type Multivariable Multiple Hypergeometric Functions. TJMCS. December 2021;13(2):359-372. doi:10.47000/tjmcs.954676
Chicago Korkmaz-duzgun, Duriye. “A New Type Multivariable Multiple Hypergeometric Functions”. Turkish Journal of Mathematics and Computer Science 13, no. 2 (December 2021): 359-72. https://doi.org/10.47000/tjmcs.954676.
EndNote Korkmaz-duzgun D (December 1, 2021) A New Type Multivariable Multiple Hypergeometric Functions. Turkish Journal of Mathematics and Computer Science 13 2 359–372.
IEEE D. Korkmaz-duzgun, “A New Type Multivariable Multiple Hypergeometric Functions”, TJMCS, vol. 13, no. 2, pp. 359–372, 2021, doi: 10.47000/tjmcs.954676.
ISNAD Korkmaz-duzgun, Duriye. “A New Type Multivariable Multiple Hypergeometric Functions”. Turkish Journal of Mathematics and Computer Science 13/2 (December 2021), 359-372. https://doi.org/10.47000/tjmcs.954676.
JAMA Korkmaz-duzgun D. A New Type Multivariable Multiple Hypergeometric Functions. TJMCS. 2021;13:359–372.
MLA Korkmaz-duzgun, Duriye. “A New Type Multivariable Multiple Hypergeometric Functions”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 2, 2021, pp. 359-72, doi:10.47000/tjmcs.954676.
Vancouver Korkmaz-duzgun D. A New Type Multivariable Multiple Hypergeometric Functions. TJMCS. 2021;13(2):359-72.