# Nonnegative linearization of orthogonal polynomials

Colloquium Mathematicae (1996)

- Volume: 69, Issue: 2, page 309-316
- ISSN: 0010-1354

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top## How to cite

topSzwarc, Ryszard. "Nonnegative linearization of orthogonal polynomials." Colloquium Mathematicae 69.2 (1996): 309-316. <http://eudml.org/doc/210345>.

@article{Szwarc1996,

author = {Szwarc, Ryszard},

journal = {Colloquium Mathematicae},

keywords = {positive linearization coefficients; third order linear differential equation; singular oscillators},

language = {eng},

number = {2},

pages = {309-316},

title = {Nonnegative linearization of orthogonal polynomials},

url = {http://eudml.org/doc/210345},

volume = {69},

year = {1996},

}

TY - JOUR

AU - Szwarc, Ryszard

TI - Nonnegative linearization of orthogonal polynomials

JO - Colloquium Mathematicae

PY - 1996

VL - 69

IS - 2

SP - 309

EP - 316

LA - eng

KW - positive linearization coefficients; third order linear differential equation; singular oscillators

UR - http://eudml.org/doc/210345

ER -

## References

top- [1] R. Askey, Linearization of the product of orthogonal polynomials, in: Problems in Analysis (R. Gunning, ed.), Princeton University Press, Princeton, N.J., 1970, 223-228.
- [2] R. Askey and S. Wainger, A dual convolution structure for Jacobi polynomials, in: Proc. Conference on Orthogonal Expansions and their Continuous Analogues, D. Haimo (ed.), Southern Illinois University Press, Carbondale, 1967, 25-36. Zbl0174.36305
- [3] R. Askey and J. A. Wilson, Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Mem. Amer. Math. Soc. 54 (1985). Zbl0572.33012
- [4] T. Chihara, An Introduction to Orthogonal Polynomials, Math. Appl. 13, Gordon and Breach, New York, 1978. Zbl0389.33008
- [5] J. Dougall, A theorem of Sonine in Bessel functions, with two extensions to spherical harmonics, Proc. Edinburgh Math. Soc. 37 (1919), 33-47.
- [6] G. Gasper, Linearization of the product of Jacobi polynomials. I, II, Canad. J. Math. 22 (1970), 171-175, 582-593. Zbl0191.35002
- [7] H. Haddad, Chain sequence preserving linear transformations, Ann. Scuola Norm. Sup. Pisa (3) 24 (1970), 78-84. Zbl0191.35304
- [8] S. Igari and Y. Uno, Banach algebras related to the Jacobi polynomials, Tôhoku Math. J. 21 (1969), 668-673. Zbl0192.48402
- [9] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343.
- [10] A. L. Schwartz, ${l}^{1}$-convolution algebras: representation and factorization, Z. Wahrsch. Verw. Gebiete 41 (1977), 161-176. Zbl0357.43004
- [11] G. Szegö, Orthogonal Polynomials, Colloq. Publ. 23, Amer. Math. Soc., Providence, R.I., 4th ed., 1975.
- [12] R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, I, SIAM J. Math. Anal. 23 (1992), 959-964. Zbl0772.42013
- [13] R. Szwarc, Orthogonal polynomials and a discrete boundary value problem, II, ibid., 965-969. Zbl0772.42014

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