دورية أكاديمية
On 2-orthogonal polynomials of Laguerre type
| العنوان: | On 2-orthogonal polynomials of Laguerre type |
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| المؤلفون: | Khalfa Douak |
| المصدر: | International Journal of Mathematics and Mathematical Sciences, Vol 22, Iss 1, Pp 29-48 (1999) |
| بيانات النشر: | Hindawi Limited, 1999. |
| سنة النشر: | 1999 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | Orthogonal polynomials, d-orthogonal polynomials, Laguerre polynomials, Sheffer polynomials, recurrence relations, integral representations., Mathematics, QA1-939 |
| الوصف: | Let {Pn}n≥0 be a sequence of 2-orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let {Qn}n≥0 be the sequence of polynomials defined by Qn:=(n+1)−1P′n+1,n≥0. When {Qn}n≥0 is, also, 2-orthogonal, {Pn}n≥0 is called classical (in the sense of having the Hahn property). In this case, both {Pn}n≥0 and {Qn}n≥0 satisfy a third-order recurrence relation (see below). Working on the recurrence coefficients, under certain assumptions and well-chosen parameters, a classical family of 2-orthogonal polynomials is presented. Their recurrence coefficients are explicitly determined. A generating function, a third-order differential equation, and a differential-recurrence relation satisfied by these polynomials are obtained. We, also, give integral representations of the two corresponding linear functionals ω0 and ω1 and obtain their weight functions which satisfy a second-order differential equation. From all these properties, we show that the resulting polynomials are an extention of the classical Laguerre's polynomials and establish a connection between the two kinds of polynomials. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 0161-1712 1687-0425 01611712 |
| العلاقة: | https://doaj.org/toc/0161-1712Test; https://doaj.org/toc/1687-0425Test |
| DOI: | 10.1155/S0161171299220297 |
| الوصول الحر: | https://doaj.org/article/cf1a5150fc674329900a11cb43ce7858Test |
| رقم الانضمام: | edsdoj.f1a5150fc674329900a11cb43ce7858 |
| قاعدة البيانات: | Directory of Open Access Journals |
Full Text Finder | تدمد: | 01611712 16870425 |
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| DOI: | 10.1155/S0161171299220297 |