# Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order

Serdica Mathematical Journal (2001)

- Volume: 27, Issue: 3, page 193-202
- ISSN: 1310-6600

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topZagorodniuk, S.. "Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order." Serdica Mathematical Journal 27.3 (2001): 193-202. <http://eudml.org/doc/11533>.

@article{Zagorodniuk2001,

abstract = {Orthonormal polynomials on the real line \{pn (λ)\} n=0 ... ∞ satisfy
the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) =
λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 =
0, λ ∈ C.
In this paper we study systems of polynomials \{pn (λ)\} n=0 ... ∞ which satisfy
the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) +
αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R,
n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1,
p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C.
It is shown that they are orthonormal on the real and the imaginary axes
in the complex plane ...},

author = {Zagorodniuk, S.},

journal = {Serdica Mathematical Journal},

keywords = {Orthogonal Polynomials; Difference Equation; orthogonal polynomials; difference equation},

language = {eng},

number = {3},

pages = {193-202},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order},

url = {http://eudml.org/doc/11533},

volume = {27},

year = {2001},

}

TY - JOUR

AU - Zagorodniuk, S.

TI - Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order

JO - Serdica Mathematical Journal

PY - 2001

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 27

IS - 3

SP - 193

EP - 202

AB - Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy
the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) =
λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 =
0, λ ∈ C.
In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy
the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) +
αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R,
n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1,
p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C.
It is shown that they are orthonormal on the real and the imaginary axes
in the complex plane ...

LA - eng

KW - Orthogonal Polynomials; Difference Equation; orthogonal polynomials; difference equation

UR - http://eudml.org/doc/11533

ER -

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