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A differential equation for multiple Bessel polynomials with raising and lowering operators

이동원|백진옥
대한수학회 (The Korean Mathematical Society)|2011.05|대한수학회보 (Bulletin of the KMS)|제48권 제3호|pp. 445-454

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키워드

differential equationmultiple orthogonal polynomialsBessel polynomialsmultiple Bessel polynomial
주제분류수학

초록

In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

Abstract

In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

참고문헌 (16)

  1. A. I. Aptekarev, "Multiple orthogonal polynomials for classical weights", Trans. Amer. Math. Soc, 355(10), pp.3887~3914 (2003)
  2. B. Beckermann, "Multiple Wilson and Jacobi-Pi~neiro polynomials", J. Approx. Theory, 13(2), pp.155~181 (2005)
  3. M. G. de Bruin, "Simultaneous Pade approximation and orthogonality, Orthogonal poly- nomials and applications (Bar-le-Duc, 1984)", Lecture Notes in Math, 1171, pp.7483~ (1985), Springer
  4. T. S. Chihara, "An Introduction to Orthogonal Polynomials" (1978), Gordon and Breach
  5. J. Coussement, "Differential equations for multiple orthogonal poly- nomials with respect to classical weights: raising and lowering operators", J. Phys. A, 39(13), pp.3311~3318 (2006)
  6. A. J. Duran, "The Stieltjes moment problem for rapidly decreasing functions", Proc. Amer. Math. Soc, 107(3), pp.731~741 (1989)
  7. 권길헌, "REAL ORTHOGONALIZING WEIGHTS FOR BESSEL POLYNOMIALS", JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 49(1-3), pp.51~57
  8. A. M. Krall, "Orthogonal polynomials through moment generating functionals", SIAM J. Math. Anal, 9(4), pp.600~603 (1978)
  9. H. L. Krall, "A new class of orthogonal polynomials: The Bessel polynomi- als", Trans. Amer. Math. Soc, 65, pp.100~115 (1949)
  10. 권길헌, "ORTHOGONALIZING WEIGHTS OF TCHEBYCHEV SETS OF POLYNOMIALS", BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 24(4), pp.361~367
  11. 권길헌, "Differential equations having orthogonal polynomial solutions", JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 80(1), pp.1~16
  12. D. W. Lee, "Properties of multiple Hermite and multiple Laguerre polynomials by the generating function", Integral Transforms Spec. Funct, 18(11), pp.855~869 (2007)
  13. D. W. Lee, "Difference equations for discrete classical multiple orthogonal polynomials", J. Approx. Theory, 150(2), pp.132~152 (2008)
  14. R. D. Morton, "Distributional weight functions for orthogonal polyno- mials", SIAM J. Math. Anal, 9(4), pp.604~626 (1978)
  15. E. M. Nikishin, "Rational Approximations and Orthogonality, Trans- lations of Mathematical Monographs", pp.92~ (1991), Amer. Math. Soc
  16. G. Szego, "Orthogonal Polynomials, 4th ed", pp.213~ (1975), Amer. Math. Soc., Colloq. Publ

관련 논문AI추천

Structure relations of classical multiple orthogonal polynomials by a generating function이동원대한수학회 · 대한수학회지2013 · 제50권 제5호The recurrence coefficients of the orthogonal polynomials with the weights $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$정해원강원경기수학회 · 한국수학논문집2017 · 제25권 제2호A NOTE ON L-CLASSICAL ORTHOGONAL POLYNOMIALSJ. O. Baek장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제3호Orthogonal polynomials satisfying partial differential equations belonging to the basic class유병훈, J. K. Lee, L. L. Littlejohn대한수학회 · 대한수학회지2004 · 제41권 제6호A New Class of Hermite-Konhauser Polynomials together with Differential EquationsMaged Gumaan Bin-Saad경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제2호Some recurrence relations of multiple orthogonal polynomials이동원대한수학회 · 대한수학회지2005 · 제42권 제4호

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