کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778843 | 1634015 | 2017 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
An elementary representation of the higher-order Jacobi-type differential equation
ترجمه فارسی عنوان
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
We investigate the differential equation for the Jacobi-type polynomials which are orthogonal on the interval [â1,1] with respect to the classical Jacobi measure and an additional point mass at one endpoint. This scale of higher-order equations was introduced by J. and R. Koekoek in 1999 essentially by using special function methods. In this paper, a completely elementary representation of the Jacobi-type differential operator of any even order is given. This enables us to trace the orthogonality relation of the Jacobi-type polynomials back to their differential equation. Moreover, we establish a new factorization of the Jacobi-type operator into a product of linear second-order operators, which gives rise to a recurrence relation with respect to the order of the equation. Finally, two interrelations with the differential equation for the symmetric ultraspherical-type polynomials are pointed out.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Indagationes Mathematicae - Volume 28, Issue 5, October 2017, Pages 976-991
Journal: Indagationes Mathematicae - Volume 28, Issue 5, October 2017, Pages 976-991
نویسندگان
Clemens Markett,