کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9509894 | 1341419 | 2005 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Generalized Zernike or disc polynomials
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We investigate generalized Zernike or disc polynomials Pm,nα(z,zâ) which are orthogonal 2D polynomials in the unit disc 0⩽zzâ<1 with weights (1âzzâ)α in complex coordinates zâ¡x+iy, zââ¡xâiy, where α>â1 is a free parameter. These polynomials can be expressed by Jacobi polynomials of transformed arguments in connection with a simple angle dependence. A limiting procedure αââ leads to Laguerre 2D polynomials Lm,n(z,zâ). Furthermore, we introduce the corresponding orthonormalized disc functions. The disc polynomials and disc functions obey two differential equations, a first-order and a second-order one with a certain degree of freedom, and the operators of lowering and raising of the indices are found. These operators can be closed to a Lie algebra su(1,1)âsu(1,1). New generating functions are derived from an operational representation which is alternative to the Rodrigues-type representation. The one-dimensional analogue of the disc polynomials which are orthogonal polynomials in the interval 0⩽r⩽1 with weight factors (1âr2)α are ultraspherical or Gegenbauer polynomials in a new standardization. The lowering and raising operators to the corresponding orthonormalized functions form a simple su(1,1) Lie algebra. This is given in the appendix in sketched form.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 174, Issue 1, 1 February 2005, Pages 135-163
Journal: Journal of Computational and Applied Mathematics - Volume 174, Issue 1, 1 February 2005, Pages 135-163
نویسندگان
Alfred Wünsche,