In mathematics, the Meixner–Pollaczek polynomials are a family of
orthogonal polynomialsP(λ) n(x,φ) introduced by
Meixner (
1934), which up to elementary changes of variables are the same as the Pollaczek polynomialsPλ n(x,a,b) rediscovered by
Pollaczek (
1949) in the case λ=1/2, and later generalized by him.
They are defined by
Examples
The first few Meixner–Pollaczek polynomials are
Properties
Orthogonality
The Meixner–Pollaczek polynomials Pm(λ)(x;φ) are orthogonal on the real line with respect to the weight function
Meixner, J. (1934), "Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion", J. London Math. Soc., s1-9: 6–13,
doi:
10.1112/jlms/s1-9.1.6
In mathematics, the Meixner–Pollaczek polynomials are a family of
orthogonal polynomialsP(λ) n(x,φ) introduced by
Meixner (
1934), which up to elementary changes of variables are the same as the Pollaczek polynomialsPλ n(x,a,b) rediscovered by
Pollaczek (
1949) in the case λ=1/2, and later generalized by him.
They are defined by
Examples
The first few Meixner–Pollaczek polynomials are
Properties
Orthogonality
The Meixner–Pollaczek polynomials Pm(λ)(x;φ) are orthogonal on the real line with respect to the weight function
Meixner, J. (1934), "Orthogonale Polynomsysteme Mit Einer Besonderen Gestalt Der Erzeugenden Funktion", J. London Math. Soc., s1-9: 6–13,
doi:
10.1112/jlms/s1-9.1.6