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Year 2021, Volume: 70 Issue: 1, 143 - 155, 30.06.2021
https://doi.org/10.31801/cfsuasmas.726225

Abstract

References

  • Adler, M., Van Moerbeke P. and Vanhaecke P., Moment matrices and multi-component KP, with applications to random matrix theory, Comm. Math. Phys, 286 (2009), 1-38.
  • Aktaş, R., Altn A. and Taşdelen, F., A new family of analytic functions dened by means of Rodrigues type formula, Math. Slovaca, 68, 3 (2018), 607-616.
  • Aktaş, R. and Altn, A., A generating function and some recurrence relations for a family of polynomials, Proceedings of the 12th WSEAS International conference on Applied Mathemat- ics, 2007, 118-121.
  • Altın, A., Aktaş, R., A class of polynomials in two variables, Mathematica Morovica, 14 (1) (2014), 1-14.
  • Aptekarev, A. I., Strong asymptotics of multiple orthogonal polynomials for Nikishin systems, Math. Sb. 190 no.5 (1999), 3-44 (Russian); Sbornik Math. 190 (5) (1999), 631-669.
  • Aptekarev, A.I., Branquinho, A. and Van Assche, W., Multiple orthogonal polynomials for classical weights, Transectional American Mathematical Society, 355,10 (2003), 3887-3914.
  • Van Assche, W. and Yakubovich, S.B., Multiple orthogonal polynomials associated with Mcdonald functions, Integral Transforms Spec. Funct., 9 (3) (2000), 229-244.
  • Van Assche, W. and Coussement, Els., Some classical multiple orthogonal polynomials, J. Comput. Appl. Math., 127 (2001), 317-347.
  • Bleher, P.M. and Kuijlaars, A.B.J., Random matrices with external source and multiple orthogonal polynomials, Internat. Math. Research Notices, 3 (2004), 109-129.
  • Coussement, E. and Van Assche, W., Multiple orthogonal polynomials associated with the modified Bessel functions of the first kind, Constructive Approximation, 19 (2003), 237-263.
  • Coussement, E. and Van Assche, W., Some properties of multiple orthogonal polynomials associated with Macdonald functions, J. Comput. Appl. Math., 133 (2001), 253-261.
  • Kaanolu, C. and Ozarslan, M.A., Some properties of generalized multiple Hermite polynomials, J. Comput. Appl. Math., 235 (2011) 4878-4887.
  • Kuijlaars, A.B.J., Van Assche, W. and Wielonsky, F., Quadratic Hermite-Pade approximation to the exponential function: a Riemann-Hilbert approach, Constr. Approx. 21 (2005), 313-320.
  • Lee, D.W., Properties of multiple Hermite and multiple Laguerre polynomials by the generating function, Integral Transforms Spec. Funct. 18 (2007) 855-869.
  • Nikishin, E.M. and Sorokin, V.V., Rational approximations and orthogonality, Translations of Mathematical Monographs (Providence, RI: American Mathematical Society), (1991), R192.
  • Ozarslan, M.A. and Kaanolu, C., Some generalization of multiple Laguerre polynomials via Rodrigues formula, Ars Combinatoria, 123 (2015) 195-206.
  • Varma, S., On a generalization of Szasz operators by multiple Appell polynomials, Stud. Univ. Babe¸s-Bolyai Math. 58 (3) (2013), 361-369.

Some properties of a new class of analytic functions defined via Rodrigues formula

Year 2021, Volume: 70 Issue: 1, 143 - 155, 30.06.2021
https://doi.org/10.31801/cfsuasmas.726225

Abstract

In this paper, we introduce and study the new family of analytic functions via Rodrigues formula. Some main properties, the generating function, various recurrence relations and differential properties of these functions are obtained. Furthermore, the differential equations are given for the subclasses of this family of analytic functions.

References

  • Adler, M., Van Moerbeke P. and Vanhaecke P., Moment matrices and multi-component KP, with applications to random matrix theory, Comm. Math. Phys, 286 (2009), 1-38.
  • Aktaş, R., Altn A. and Taşdelen, F., A new family of analytic functions dened by means of Rodrigues type formula, Math. Slovaca, 68, 3 (2018), 607-616.
  • Aktaş, R. and Altn, A., A generating function and some recurrence relations for a family of polynomials, Proceedings of the 12th WSEAS International conference on Applied Mathemat- ics, 2007, 118-121.
  • Altın, A., Aktaş, R., A class of polynomials in two variables, Mathematica Morovica, 14 (1) (2014), 1-14.
  • Aptekarev, A. I., Strong asymptotics of multiple orthogonal polynomials for Nikishin systems, Math. Sb. 190 no.5 (1999), 3-44 (Russian); Sbornik Math. 190 (5) (1999), 631-669.
  • Aptekarev, A.I., Branquinho, A. and Van Assche, W., Multiple orthogonal polynomials for classical weights, Transectional American Mathematical Society, 355,10 (2003), 3887-3914.
  • Van Assche, W. and Yakubovich, S.B., Multiple orthogonal polynomials associated with Mcdonald functions, Integral Transforms Spec. Funct., 9 (3) (2000), 229-244.
  • Van Assche, W. and Coussement, Els., Some classical multiple orthogonal polynomials, J. Comput. Appl. Math., 127 (2001), 317-347.
  • Bleher, P.M. and Kuijlaars, A.B.J., Random matrices with external source and multiple orthogonal polynomials, Internat. Math. Research Notices, 3 (2004), 109-129.
  • Coussement, E. and Van Assche, W., Multiple orthogonal polynomials associated with the modified Bessel functions of the first kind, Constructive Approximation, 19 (2003), 237-263.
  • Coussement, E. and Van Assche, W., Some properties of multiple orthogonal polynomials associated with Macdonald functions, J. Comput. Appl. Math., 133 (2001), 253-261.
  • Kaanolu, C. and Ozarslan, M.A., Some properties of generalized multiple Hermite polynomials, J. Comput. Appl. Math., 235 (2011) 4878-4887.
  • Kuijlaars, A.B.J., Van Assche, W. and Wielonsky, F., Quadratic Hermite-Pade approximation to the exponential function: a Riemann-Hilbert approach, Constr. Approx. 21 (2005), 313-320.
  • Lee, D.W., Properties of multiple Hermite and multiple Laguerre polynomials by the generating function, Integral Transforms Spec. Funct. 18 (2007) 855-869.
  • Nikishin, E.M. and Sorokin, V.V., Rational approximations and orthogonality, Translations of Mathematical Monographs (Providence, RI: American Mathematical Society), (1991), R192.
  • Ozarslan, M.A. and Kaanolu, C., Some generalization of multiple Laguerre polynomials via Rodrigues formula, Ars Combinatoria, 123 (2015) 195-206.
  • Varma, S., On a generalization of Szasz operators by multiple Appell polynomials, Stud. Univ. Babe¸s-Bolyai Math. 58 (3) (2013), 361-369.
There are 17 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Articles
Authors

Halil Gezer 0000-0002-1248-989X

Cem Kaanoglu This is me 0000-0001-7733-041X

Publication Date June 30, 2021
Submission Date April 24, 2020
Acceptance Date November 20, 2020
Published in Issue Year 2021 Volume: 70 Issue: 1

Cite

APA Gezer, H., & Kaanoglu, C. (2021). Some properties of a new class of analytic functions defined via Rodrigues formula. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 143-155. https://doi.org/10.31801/cfsuasmas.726225
AMA Gezer H, Kaanoglu C. Some properties of a new class of analytic functions defined via Rodrigues formula. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):143-155. doi:10.31801/cfsuasmas.726225
Chicago Gezer, Halil, and Cem Kaanoglu. “Some Properties of a New Class of Analytic Functions Defined via Rodrigues Formula”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 143-55. https://doi.org/10.31801/cfsuasmas.726225.
EndNote Gezer H, Kaanoglu C (June 1, 2021) Some properties of a new class of analytic functions defined via Rodrigues formula. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 143–155.
IEEE H. Gezer and C. Kaanoglu, “Some properties of a new class of analytic functions defined via Rodrigues formula”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 143–155, 2021, doi: 10.31801/cfsuasmas.726225.
ISNAD Gezer, Halil - Kaanoglu, Cem. “Some Properties of a New Class of Analytic Functions Defined via Rodrigues Formula”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 143-155. https://doi.org/10.31801/cfsuasmas.726225.
JAMA Gezer H, Kaanoglu C. Some properties of a new class of analytic functions defined via Rodrigues formula. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:143–155.
MLA Gezer, Halil and Cem Kaanoglu. “Some Properties of a New Class of Analytic Functions Defined via Rodrigues Formula”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 143-55, doi:10.31801/cfsuasmas.726225.
Vancouver Gezer H, Kaanoglu C. Some properties of a new class of analytic functions defined via Rodrigues formula. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):143-55.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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