scholarly journals Algebraic computation of resolvents without extraneous powers

2012 ◽  
Vol 33 (7) ◽  
pp. 1369-1385 ◽  
Author(s):  
Philippe Aubry ◽  
Annick Valibouze
Keyword(s):  
Algebraic Computation

scholarly journals New Specific and General Linearization Formulas of Some Classes of Jacobi Polynomials

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 74
Author(s):  
Waleed Mohamed Abd-Elhameed ◽  
Afnan Ali
Keyword(s):  
Chebyshev Polynomials ◽  
Hypergeometric Functions ◽  
Jacobi Polynomials ◽  
Algebraic Computation ◽  
Ultraspherical Polynomials ◽  
Current Article ◽  
Linearization Coefficients

The main purpose of the current article is to develop new specific and general linearization formulas of some classes of Jacobi polynomials. The basic idea behind the derivation of these formulas is based on reducing the linearization coefficients which are represented in terms of the Kampé de Fériet function for some particular choices of the involved parameters. In some cases, the required reduction is performed with the aid of some standard reduction formulas for certain hypergeometric functions of unit argument, while, in other cases, the reduction cannot be done via standard formulas, so we resort to certain symbolic algebraic computation, and specifically the algorithms of Zeilberger, Petkovsek, and van Hoeij. Some new linearization formulas of ultraspherical polynomials and third-and fourth-kinds Chebyshev polynomials are established.

Logic and algebraic computation

1984 ◽  
Vol 18 (2) ◽  
pp. 26-26 ◽  
Author(s):  
Wolfgang Bibel
Keyword(s):  
Algebraic Computation

scholarly journals Lie algebraic computation

1996 ◽  
Vol 97 (1-2) ◽  
pp. 53-62 ◽  
Author(s):  
A.M. Cohen ◽  
W.A. de Graaf
Keyword(s):  
Algebraic Computation
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