T. S. Chihara, A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials, Canad. Math. Bull. 13,4 (1970), 529--532. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
From Discrete to Absolutely Continuous Solutions of Indeterminate.. - Berg (1998) (1 citation) (Correct)
....as s n (d oe ) q ; n 0; 2.3) where 0 q 1 is defined by q = e Gammaoe . Stieltjes showed that the moments (2.3) belong to an indeterminate moment problem by pointing out that all the densities (s 2 [ Gamma1; 1] d oe (x) 1 s sin( log x) have the same moments (2. 3) Chihara [10] and later Leipnik [19] gave the following family of discrete measures with the moments (2.3) For a 0 define the discrete probability L(a) 2.5) It is easy to calculate the moments of a using the translation invariance of P 1 Gamma1 . In fact s n ( a ) ....
T. S. Chihara, A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials, Canad. Math. Bull. 13,4 (1970), 529--532.
On Some Indeterminate Moment Problems for Measures on a Geometric.. - Berg (1998) (1 citation) (Correct)
....the factor x Gamma1 in (2.1) Stieltjes showed the indeterminacy of (2.3) by remarking that all the densities (s 2 [ Gamma1; 1] d oe (x) 1 s sin( 2 oe 2 log x) have the same moments (2. 3) cf. 20] The crucial point in the calculation is the Z periodicity of sin(2 x) Chihara [6] and later Leipnik [15] gave the following family of solutions to (2.3) concentrated on countable sets. For a 0 define the measure H a = 1 c(a) 1 X k= Gamma1 a k q k 2 aq 2k (2.4) concentrated on (a) faq 2k j k 2 Zg, where c(a) 1 X k= Gamma1 a k q k 2 : 2.5) Note ....
T. S. Chihara, A characterization and a class of distribution functions for the Stieltjes-Wigert polynomials, Canad. Math. Bull. 13,4 (1970), 529--532.
The impact of Stieltjes' work on continued fractions and.. - Valent, VAN ASSCHE (1995) (2 citations) (Correct)
.... Gamman 0 ; q ; Gammaxq n 1 ; and the latter polynomials are the ones given in [25] Using the weight function in [25] and taking into account the scaling x 7 x p q gives the weight function 1 ( Gammax p q; q) 1 ( Gamma p q=x; q) 1 ; 0 x 1: Chihara has weight functions like this [9]. Stieltjes was aware that the special choice q = e Gamma1=2 was not the only possible choice and explicitly mentions that it sufficies to have q 1. StieltjesWigert polynomials are also limit cases of q Laguerre polynomials, as was shown by Askey [3] These q Laguerre polynomials are also ....
T. S. Chihara, A characterization and a class of distribution functions for the Stieltjes Wigert polynomials, Canad. Math. Bull. 13 (1970), 529--532.
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