Treffer: Reverse generalized Bessel matrix differential equation, polynomial solutions, and their properties

Title:
Reverse generalized Bessel matrix differential equation, polynomial solutions, and their properties
Authors:
M. Abul-Dahab, M. Abul‐Ez, Z. M. G. Kishka, Denis Constales
Source:
Mathematical Methods in the Applied Sciences. 38:1005-1013
Publisher Information:
Wiley, 2013.
Publication Year:
2013
Subject Terms:
Composite material, Matrix function, Orthogonal polynomials, Matrix (chemical analysis), Symmetric matrix, Generalization, Geometry, Pascal matrix, Matrix Valued Polynomials, Polynomial, Mathematical analysis, Quantum mechanics, 01 natural sciences, Orthogonal Polynomials, Gegenbauer polynomials, Differential equation, FOS: Mathematics, Bessel polynomials, Bessel function, 0101 mathematics, Scalar (mathematics), Wilson polynomials, Matrix Algorithms and Iterative Methods, Eigenvalues and eigenvectors, Struve function, Applied Mathematics, Physics, 4. Education, Classical orthogonal polynomials, Pure mathematics, Statistical and Nonlinear Physics, Applied mathematics, 16. Peace & justice, Materials science, Matrix polynomial, Computational Theory and Mathematics, Physics and Astronomy, Computer Science, Physical Sciences, Jacobi polynomials, Square matrix, Polynomial matrix, Mathematics, Rogue Waves in Nonlinear Systems
Document Type:
Fachzeitschrift Article<br />Other literature type
Language:
English
ISSN:
0170-4214
DOI:
10.1002/mma.3020
DOI:
10.60692/p7yah-cbc50
DOI:
10.60692/t00ab-efg39
Access URL:
https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mma.3020
https://ui.adsabs.harvard.edu/abs/2015MMAS...38.1005A/abstract
https://onlinelibrary.wiley.com/doi/full/10.1002/mma.3020
https://biblio.ugent.be/publication/7177752
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....ab73d69b4dd94c7c1d91e56fb542d971
Database:
OpenAIRE

Weitere Informationen

Cet article est consacré à l'étude des polynômes matriciels de Bessel généralisés inverses (RGBMP) au sein de l'analyse complexe. Cette étude est supposée être une généralisation et une amélioration du cas scalaire dans le cadre de la matrice. Nous donnons une définition des polynômes matriciels de Bessel généralisés inverses Θn(A ; B ; z), , pour les matrices de paramètres (carrés) A et B, et fournissons une équation différentielle matricielle du second ordre satisfaite par ces polynômes. Par la suite, une formule de type Rodrigues, une relation de récurrence matricielle et une fonction pseudo-génératrice sont ensuite développées pour les RGBMP. © 2013 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.
Este artículo está dedicado al estudio de los polinomios de matriz de Bessel generalizados inversos (RGBMP) dentro del análisis complejo. Se supone que este estudio es una generalización y mejora del caso escalar en el entorno de la matriz. Damos una definición de los polinomios de matriz de Bessel generalizados inversos Θn(A; B; z), , para las matrices de parámetros (cuadradas) A y B, y proporcionamos ecuaciones diferenciales de matriz de segundo orden satisfechas por estos polinomios. Posteriormente, se desarrollan una fórmula de tipo Rodrigues, una relación de recurrencia de matriz y una función pseudogeneradora para los RGBMP. © 2013 The Authors Mathematical Methods in the Applied Sciences Publicado por John Wiley & Sons, Ltd.
This paper is devoted to the study of reverse generalized Bessel matrix polynomials (RGBMPs) within complex analysis. This study is assumed to be a generalization and improvement of the scalar case into the matrix setting. We give a definition of the reverse generalized Bessel matrix polynomials Θn(A; B; z), , for parameter (square) matrices A and B, and provide a second-order matrix differential equations satisfied by these polynomials. Subsequently, a Rodrigues-type formula, a matrix recurrence relationship, and a pseudo-generating function are then developed for RGBMPs. © 2013 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.
هذه الورقة مخصصة لدراسة متعددات حدود مصفوفة بسل المعممة العكسية (RGBMPs) ضمن التحليل المعقد. يُفترض أن تكون هذه الدراسة تعميمًا وتحسينًا للحالة العددية في إعداد المصفوفة. نقدم تعريفًا لكثيرات حدود مصفوفة بيسل المعممة العكسية (A; B; z)، لمصفوفات المتغير (المربع) A و B، ونقدم معادلات تفاضلية للمصفوفة من الدرجة الثانية مستوفاة بهذه متعددات الحدود. بعد ذلك، يتم تطوير صيغة من نوع رودريغز، وعلاقة تكرار المصفوفة، ووظيفة توليد زائفة لـ RGBMPs. © 2013 The Authors Mathematical Methods in the Applied Sciences Published by John Wiley & Sons, Ltd.