Some Properties of Sobolev Orthogonal Polynomials Associated with Chebyshev Polynomials of the Second Kind

2021 ◽  
pp. 259-273
Author(s):  
M. S. Sultanakhmedov
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Sobolev Orthogonal Polynomials

scholarly journals Neoteric formulas of the monic orthogonal Chebyshev polynomials of the sixth-kind involving moments and linearization formulas

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Waleed M. Abd-Elhameed ◽  
Youssri H. Youssri
Keyword(s):  
Orthogonal Polynomials ◽  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Connection Coefficients ◽  
Current Article ◽  
In Virtue Of ◽  
Connection Formulas

AbstractThe principal aim of the current article is to establish new formulas of Chebyshev polynomials of the sixth-kind. Two different approaches are followed to derive new connection formulas between these polynomials and some other orthogonal polynomials. The connection coefficients are expressed in terms of terminating hypergeometric functions of certain arguments; however, they can be reduced in some cases. New moment formulas of the sixth-kind Chebyshev polynomials are also established, and in virtue of such formulas, linearization formulas of these polynomials are developed.

scholarly journals Asymptotics for Jacobi–Sobolev orthogonal polynomials associated with non-coherent pairs of measures

2010 ◽  
Vol 162 (11) ◽  
pp. 1945-1963 ◽  
Author(s):  
Eliana X.L. de Andrade ◽  
Cleonice F. Bracciali ◽  
Laura Castaño-García ◽  
Juan J. Moreno-Balcázar
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Orthogonal Polynomials ◽  
Coherent Pairs

Orthogonal polynomials: applications and computation

Acta Numerica ◽  
1996 ◽  
Vol 5 ◽  
pp. 45-119 ◽  
Author(s):  
Walter Gautschi
Keyword(s):  
Numerical Methods ◽  
Weight Function ◽  
Orthogonal Polynomials ◽  
Rational Function ◽  
Recurrence Relations ◽  
Recurrence Coefficients ◽  
Basic Task ◽  
Sobolev Orthogonal Polynomials ◽  
Gauss Type ◽  
Three Term Recurrence Relation

We give examples of problem areas in interpolation, approximation, and quadrature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the orthogonal polynomials. This can be done by methods relying either on moment information or on discretization procedures. The effect on the recurrence coefficients of multiplying the weight function by a rational function is also discussed. Similar methods are applicable to computing Sobolev orthogonal polynomials, although their recurrence relations are more complicated. The paper concludes with a brief account of available software.

scholarly journals General Sobolev Orthogonal Polynomials

1996 ◽  
Vol 200 (3) ◽  
pp. 614-634 ◽  
Author(s):  
Francisco Marcellán ◽  
Teresa E. Pérez ◽  
Miguel A. Piñar ◽  
André Ronveaux
Keyword(s):  
Orthogonal Polynomials ◽  
Sobolev Orthogonal Polynomials
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