Formulas for Elementary Spherical Functions and Generalized Jacobi Polynomials

1984 ◽  
Vol 15 (4) ◽  
pp. 805-833 ◽  
Author(s):  
Lars Vretare
Keyword(s):  
Jacobi Polynomials ◽  
Spherical Functions ◽  
Generalized Jacobi Polynomials

scholarly journals Generalized Jacobi polynomials

1936 ◽  
Vol 42 (12) ◽  
pp. 901-909 ◽  
Author(s):  
D. N. Sen ◽  
V. Rangachariar
Keyword(s):  
Jacobi Polynomials ◽  
Generalized Jacobi Polynomials

scholarly journals Some Algorithms for Solving Third-Order Boundary Value Problems Using Novel Operational Matrices of Generalized Jacobi Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
W. M. Abd-Elhameed
Keyword(s):  
Boundary Value Problems ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
Operational Matrix ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Third Order ◽  
Generalized Jacobi Polynomials ◽  
Nonlinear Algebraic Equations ◽  
Derivatives Of

The main aim of this research article is to develop two new algorithms for handling linear and nonlinear third-order boundary value problems. For this purpose, a novel operational matrix of derivatives of certain nonsymmetric generalized Jacobi polynomials is established. The suggested algorithms are built on utilizing the Galerkin and collocation spectral methods. Moreover, the principle idea behind these algorithms is based on converting the boundary value problems governed by their boundary conditions into systems of linear or nonlinear algebraic equations which can be efficiently solved by suitable solvers. We support our algorithms by a careful investigation of the convergence analysis of the suggested nonsymmetric generalized Jacobi expansion. Some illustrative examples are given for the sake of indicating the high accuracy and efficiency of the two proposed algorithms.

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