MRM-applicable orthogonal polynomials for certain hypergeometric functions
نویسندگان
چکیده
منابع مشابه
Mrm-applicable Orthogonal Polynomials for Certain Hypergeometric Functions
The multiplicative renormalization method (MRM) is intorduced to obtain generating functions of orthogonal polynomials of given probability measures. Complete lists of MRM-applicable measures for MRM-factors h(x) = ex and (1 − x)−· were obtained recently. On the other hand, it is known that gamma distributions have at least two types of MRM-factors h(x) = 0F1(−;·;x) and h(x) = 1F1(c;·;x). The u...
متن کاملBasic Hypergeometric Functions and Orthogonal Laurent Polynomials
A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials { 2Φ1(q−n, qb+1; q−c+b−n; q, qz)}n=0, where 0 < q < 1 and the complex parameters b, c and d are such that b = −1,−2, . . ., c− b+ 1 = −1,−2, . ...
متن کاملOrthogonal basic hypergeometric Laurent polynomials
The Askey-Wilson polynomials are orthogonal polynomials in x = cos θ, which are given as a terminating 4φ3 basic hypergeometric series. The non-symmetric AskeyWilson polynomials are Laurent polynomials in z = eiθ, which are given as a sum of two terminating 4φ3’s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single 4φ3’s which are Laurent polynomials in...
متن کاملComplexity analysis of hypergeometric orthogonal polynomials
The complexity measures of the Crámer-Rao, Fisher-Shannon and LMC (López-Ruiz, Mancini and Calvet) types of the Rakhmanov probability density ρn(x) = ω(x)p 2 n(x) of the polynomials pn(x) orthogonal with respect to the weight function ω(x), x ∈ (a, b), are used to quantify various two-fold facets of the spreading of the Hermite, Laguerre and Jacobi systems all over their corresponding orthogona...
متن کاملOn Bc Type Basic Hypergeometric Orthogonal Polynomials
Abstract. The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partially discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Stochastic Analysis
سال: 2009
ISSN: 0973-9599
DOI: 10.31390/cosa.3.3.05