323,882 research outputs found
Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations
No full textWe investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations. It is shown that the coefficients in these recurrence relations can be expressed in terms of Wronskians of modified Bessel functions and confluent hypergeometric functions, respectively for the generalized Charlier and generalized Meixner polynomials. These Wronskians arise in the description of special function solutions of the third and fifth Painlevé equations
Cheliplana caeca Meixner 1938
No full textCheliplana caeca Meixner, 1938 The name Cheliplana caeca was used by Meixner (1938) to refer to a species of Cheliplana with strongly curved proboscis hooks and a thick ‘cuticle’ lining the prepharyngeal tube. As noted by Marcus (1952), who refrained from including C. caeca in his key to Karkinorhynchidae, both the male and female genital structures are unknown, making it impossible to identify the species in the future. It is therefore considered a nomen nudum.Published as part of Gobert, Stefan, Diez, Yander L., Monnens, Marlies, Reygel, Patrick, Van Steenkiste, Niels W. L., Leander, Brian S. & Artois, Tom, 2021, A revision of the genus Cheliplana de Beauchamp, 1927 (Rhabdocoela: Schizorhynchia), with the description of six new species, pp. 453-494 in Zootaxa 4970 (3) on page 486, DOI: 10.11646/zootaxa.4970.3.2, http://zenodo.org/record/476669
Asymptotic Formulas for the Zeros of the Meixner Polynomials
No full textAbstractThe zeros of the Meixner polynomialmn(x;β,c) are real, distinct, and lie in (0,∞). Letαn,sdenote thesth zero ofmn(nα;β,c), counted from the right; and letαn,sdenote thesth zero ofmn(nα;β,c), counted from the left. For each fixeds, asymptotic formulas are obtained for bothαn,sandαn,s, asn→∞
On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight
No full textThis paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an exponential deformation of the classical Meixner–Pollaczek measure. In this contribution, we investigate certain properties such as moments of finite order, some new recursive relations, concise formulations, differential-recurrence relations, integral representation and some properties of the zeros (quasi-orthogonality, monotonicity and convexity of the extreme zeros) of the corresponding perturbed polynomials. Some auxiliary results for Meixner–Pollaczek polynomials are revisited. Some applications such as Fisher’s information, Toda-type relations associated with these polynomials, Gauss–Meixner–Pollaczek quadrature as well as their role in quantum oscillators are also reproduced
On certain properties and applications of the perturbed Meixner–Pollaczek weight
No full textThis paper deals with monic orthogonal polynomials orthogonal with a perturbation
of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek
polynomials, are described by their weight function emanating from an exponential deformation
of the classical Meixner–Pollaczek measure. In this contribution, we investigate certain properties
such as moments of finite order, some new recursive relations, concise formulations, differentialrecurrence
relations, integral representation and some properties of the zeros (quasi-orthogonality,
monotonicity and convexity of the extreme zeros) of the corresponding perturbed polynomials.
Some auxiliary results for Meixner–Pollaczek polynomials are revisited. Some applications such
as Fisher’s information, Toda-type relations associated with these polynomials, Gauss–Meixner–
Pollaczek quadrature as well as their role in quantum oscillators are also reproduced.The NMU Council postdoctoral fellowshiphttps://www.mdpi.com/journal/mathematicsam2022Mathematics and Applied Mathematic
Trechus priapus subsp. medius Meixner 1939
No full textTrechus priapus medius Meixner, 1939 References. Trechus priapus medius: Guéorguiev 1998: 40 (Osogovo: Ruen). Material studied. Osogovo Mountain, Sultan Tepe (Carev Vrv), 2000m, mountain pasture, 17.07.2007, 1 s., leg. S. Hristovski (cSH); Osogovo mountain, Kalin Kamen, Altan Češma, 1850m, peatbog, 12.06 – 10.08 –2008, 2 s., leg. S. Hristovski (cSH); Osogovo mountain, Ruen, 2252m, peatbog, 13.06.2009, 15 s., leg. S. Hristovski (cSH). Distribution. 83.Published as part of Hristovski, Slavčo & Guéorguiev, Borislav, 2015, Annotated catalogue of the carabid beetles of the Republic of Macedonia (Coleoptera: Carabidae), pp. 1-190 in Zootaxa 4002 (1) on page 73, DOI: 10.11646/zootaxa.4002.1.1, http://zenodo.org/record/23894
The Symmetric Meixner-Pollaczek polynomials
No full textThe Symmetric Meixner-Pollaczek polynomials are considered. We denote these polynomials in this thesis by pn(λ)(x) instead of the standard notation pn(λ) (x/2, π/2), where λ > 0. The limiting case of these sequences of polynomials pn(0) (x) =limλ→0 pn(λ)(x), is obtained, and is shown to be an orthogonal sequence in the strip, S = {z ∈ ℂ : −1≤ℭ (z)≤1}. From the point of view of Umbral Calculus, this sequence has a special property that makes it unique in the Symmetric Meixner-Pollaczek class of polynomials: it is of convolution type. A convolution type sequence of polynomials has a unique associated operator called a delta operator. Such an operator is found for pn(0) (x), and its integral representation is developed. A convolution type sequence of polynomials may have associated Sheffer sequences of polynomials. The set of associated Sheffer sequences of the sequence pn(0)(x) is obtained, and is found to be ℙ = {{pn(λ) (x)} =0 : λ ∈ R}. The major properties of these sequences of polynomials are studied. The polynomials {pn(λ) (x)}∞n=0, λ < 0, are not orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard’s three term recurrence relation condition. For every λ ≤ 0, an associated nonstandard inner product is defined with respect to which pn(λ)(x) is orthogonal. Finally, the connection and linearization problems for the Symmetric Meixner-Pollaczek polynomials are solved. In solving the connection problem the convolution property of the polynomials is exploited, which in turn helps to solve the general linearization problem
Some new results for Charlier and Meixner polynomials
No full textAbstractIn Bavinck (1996), we proved the following general result for Laguerre polynomials. For all x,α ∈C∑k=jiksL(-α-i-1)i−k(−x)L(α+j)k−j (x)=σi, 2s+j(−x)s, i,j,s∈{0,1,2,…} provided that i ⩾ 2s + j. In this letter we derive the analogues of this formula for Charlier and Meixner polynomials
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