On Gauss-Type Quadrature Rules

REFERENCES

• M.I. Bueno and F.M. Dopico ( 2007 ). A more accurate algorithm for computing the Christoffel transformation . J. Comp. Appl. Math. 205 ( 1 ): 567 – 582 .
   Google Scholar
• M.A. Chaudhry and A. Qadir (2007). Identity-type functions and polynomials. Int. J. Math. & Math. Sci. 4:1–10.
   Google Scholar
• E.B. Christoffel ( 1858 ). Uber die Gaubische Quadratur und eine Verallgemeinerung derselben . J. Reine Angew. Math. 55 : 61 – 82 .
   Google Scholar
• P.J. Davis and P. Rabinowitz ( 1984 ). Methods of Numerical Integration . 2nd ed. , Academic Press .
   Google Scholar
• D. Galant ( 1971 ). An implementation of Christoffel's theorem in the theory of orthogonal polynomials . Math. Comput. 25 : 111 – 113 .
   Google Scholar
• W. Gautschi ( 1982 ). An algorithmic implementation of the generalized Christoffel theorem. In: Numerical Intergration (G. Hammerlin, ed.) . Internat. Ser. Numer. Math. 57 : 89 – 106 .
   Google Scholar
• W. Gautschi ( 1996 ). Orthogonal Polynomials: applications and computation . Acta Numerica. 5 : 45 – 119 .
   Google Scholar
• W. Gautschi ( 2000 ). Gauss–Radau formulae for Jacobi and Laguerre weight functions . Mathematics and Computers in Simulation. 54 : 403 – 412 .
   Google Scholar
• W. Gautschi ( 2000 ). High-order Gauss–Lobatto formulae . Numerical Algolrithms 25 : 213 – 222 .
   Google Scholar
• W. Gautschi ( 2004 ). Orthogonal Polynomials: Computation and Approximation . Oxford University Press , Oxford .
   Google Scholar
• W. Gautschi and S. Li ( 1991 ). Gauss–Radau and Gauss–Lobatto quadratures with double end points . J. Comp. Appl. Math. 34 ( 3 ): 343 – 360 .
   Google Scholar
• Ya. L. Geronimua ( 1940 ). On the polynomials orthogonal with respect to a given number sequence . Zap. Mat. Otdel. Khar'kov. Univers. I NII Mat. I Mehan. 17 : 3 – 18 .
   Google Scholar
• G.H. Golub ( 1973 ). Some modified matrix eigenvalue problems . SIAM Rev. 15 : 318 – 334 .
   Web of Science ®Google Scholar
• G.H. Golub and J. Kautsky ( 1983 ). Calculation of Gauss quadratures with multiple free and fixed knots . Numer. Math. 41 : 147 – 163 .
   Google Scholar
• G.H. Golub and J.H. Welsh ( 1969 ). Calculation of Gauss quadrature rules . Math. Comp. 23 : 221 – 230 .
   Web of Science ®Google Scholar
• I.S. Gradshteyn and I. M. Ryzhik ( 1994 ). Tables of Integrals, Series and Products . ( A. Jeffrey ed.). Academic Press .
   Google Scholar
• M. Ismail ( 2005 ). Classical and Quantum Polynomials in One Variable . Encyclop. Math. Its Appl. , Vol. 28 . Cambridge Univ. Press , UK .
   Google Scholar
• J. Kautsky and G.H. Golub ( 1983 ). On the calculation of Jacobi Matrices . Linear Algebra Appl. 52/53 : 439 – 455 .
   Google Scholar
• D.P. Laurie ( 1997 ). Calculation of Gauss-Kronrod quadrature rules . Math. Comp. 66 : 1133 – 1145 .
   Web of Science ®Google Scholar
• S. Li ( 1996 ). Kronrod extension of generalized Gauss–Radau and Gauss–Lobatto formulae . Rocky Mountain J. Math. 26 ( 4 ): 1455 – 1472 .
   Google Scholar
• Masjed-Jamei , M. Eslahchi and M. Dehghan ( 2005 ). On numerical improvement of Gauss–Radau quadrature rules . Appl. Math. Computation. 168 : 51 – 64 .
   Google Scholar
• C.B. Mler ( 2004 ). Numerical Computing with MATLAB. SIAM.
   Google Scholar
• G. Recktenwald ( 2000 ). Numerical Methods with MATLAB: Implementation and Application . Prentice Hall .
   Google Scholar
• E.D. Rainville ( 1971 ). Special Functions . Chelsea , New York .
   Google Scholar
• E.D. Rainville , Ph. E.R. Bedient , and E. Bedient ( 1997 ). Elementary Differential Equations . Prentice Hall .
   Google Scholar
• L.J. Slater ( 1966 ). Generalized Hypergeometric Functions . Cambridge University Press , Cambridge , UK .
   Google Scholar
• H.S. Wilf ( 1962 ). Mathematics for Physical Sciences . Wiley .
   Google Scholar