Product-Integration Rules Based on the Zeros of Jacobi Polynomials

1980 ◽  
Vol 17 (1) ◽  
pp. 1-13 ◽  
Author(s):  
William E. Smith ◽  
Ian H. Sloan
Keyword(s):  
Jacobi Polynomials ◽  
Product Integration ◽  
Integration Rules

scholarly journals Numerical Simulations and FPGA Implementations of Fractional-Order Systems Based on Product Integration Rules

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 102093-102105 ◽  
Author(s):  
Amr M. Abdelaty ◽  
Merna Roshdy ◽  
Lobna A. Said ◽  
Ahmed G. Radwan
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Product Integration ◽  
Integration Rules

scholarly journals Interpolatory product integration for Riemann-integrable functions

1987 ◽  
Vol 29 (2) ◽  
pp. 195-202 ◽  
Author(s):  
Philip Rabinowitz ◽  
William E. Smith
Keyword(s):  
Orthogonal Polynomials ◽  
Integration Interval ◽  
Product Integration ◽  
Zeros Of Orthogonal Polynomials ◽  
Integrable Functions ◽  
Riemann Integrable Functions ◽  
Integration Rules

AbstractConditions are fround for the convergence of intepolatory product integration rules and the corresponding companion rules for the class of Riemann-integrable functions. These condtions are used to prove convergence for several classes of rules based on sets of zeros of orthogonal polynomials possibly augmented by one both of the endpoints of the integration interval.

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