Mean-value formulae for integrals involving generalized orthogonal polynomials

Laura Gori; D. D. Stancu

Authors

Laura Gori "La Sapienza" University, Roma, Italy
D. D. Stancu "Babeş Bolyai" University, Cluj-Napoca, Romania

Abstract views: 157

Abstract

Not available.

Downloads

Download data is not yet available.

References

S. Bernstein , Sur les polynômes orthogonaux relatifs à un segment fini, J. Math. Pures Appl. (9) 9 (1930), pp.127-177.

L. Chakalov, General quadrature formulae of Gaussian type, Bulgar. Akad. Nauk. lzv. Mat. Inst. 1 (1954), pp. 67-84.

N. Cioranescu, Une généralisation de la première formule de Ia moyenne et des polynômes de Tchebychev, C.R. Acad. Sci. Paris 206 (1938), pp. 1182-1784.

. W. Gautschi, A Survey of Gauss-ChristoffeI Quadrature Formulae, In: E. B. Christoffel, P. L. Butzer, F. Fehér, (Eds), Birkhäuser, Basel, 1981, pp. pp. 72-147, https://doi.org/10.1007/978-3-0348-5452-8_6

A. Ghizzetti and A. Ossicinii, Guadrature Formulae, ISNM 3, Birkhäuser, Basel, 1970.

A. Ghizzetti and A. Ossicini, Generalízzazione dei polinomi s-orthogonali Atti Acad. Sci. Torino 109 (1974/1975), pp. 371-379.

A. Ghizzetti and A. Oossicini, Sulle esistenza e unicità delle formule di quadratura gaussiana, Rend. Mat. (6) 8 (1975), pp.1-15.

L. Gori, On the Behaviour oftlheZzeros of s-Orthogonal Polynonials, ln: on orthogonal Polynomials and Their Applications, Monogr. Acad. Ciecias, Zaragoza, 1988, pp.71-85.

L. Gori and E. Santi, On the convergence of Turán type rules for Cauchy principal value integrals, Calcolo 28 (1991), pp. 21-35, https://doi.org/10.1007/bf02575867

L. Gori, M. L. Lo Cascio and G.V. Milanović, The σ-Orthogonal Polynomials: A Method of construction, In: Orthogonal Polynonials and Their Applications, C. Brezinski', L. Gori, A. Ronveaux, (Eds), Baltzer AG Sci. Publ., IMACS, 1991, pp. 281-285.

L. Gori and C. A. Micchelli, On weight functions which admit explicit Gauss-Turán quadrature formulas, Math. Comput. 69 (1996), pp. 1567-1581, https://doi.org/10.1090/s0025-5718-96-00769-7

D. Jackson, On the method of least mth powers for a set of so,i;tamepis equations, Ann. Math. 12 (1924), pp.184-252, https://doi.org/10.2307/1967908

A. Lupaş, Teoreme de medie pentru coeficienţii Fourier-Jacobi, Rev. Anal. Numer. Theorie Approximation 3 (1974), pp. 79-84.

G. V. Milovanović, Construction of s-Orthogonal Polynomials and Turán Quadratures, In:Numer. Methods and Approx. Theory III (Niš 1987), D. V. Milovanović, (Ed.), Univ, Niš, 1988, pp. 311-388.

A. Morelli and and A. Verna, Alcune proprietà degli zeri dei polinomi σ-ortogonali, Rend. Mat. Appt.1 (1987), pp.43-52.

A. Ossicini and F. Rosati, Sulla convergenza dei funzionali ipergaussiani, Rend. Mat.6 (1978), pp. 97-108.

T. Popoviciu, Sur la distribution des zéros de certains polynômes minimisants, Bull. Acad. Roumaine 16 (1934), pp. 214-217.

T. Popoviciu, On a generalizalion of the numerical integration formula of Gauss, Acad. R. P. Române, Iaşi, St. cerc, şt. 6 (1955), pp.29-57.

T, Popoviciu, .Sur le reste dans certaines formules linéaires d'approximation de I'analyse, Mathematica (Cluj) 1 (24) (1959), pp.95-142.

D. D. Stancu, Sur quelques formules générales de quadrature du type Gauss-Christoffel, Mathematica (Cluj) I (24) (1959), pp.167-182.

D.D. Stancu, On Hermite's osculatory interpolation formula and on some generalizations of it, Mathematica (Cluj) 8 (31) (1966), pp. 373-391.

D. D. Stancu and M. R. Occorsio, Mean-value Formulae for Integrals Obtained by Using Gaussian-type Quadratures, Suppl. Rend. Circolo Matematico di Palermo, Ser II, No. 33, 1993, pp. 463-478.

G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ. 23 (1939), New York.

P. Turán, On the theory of the mechanical quadrature, Acta Sci. Math. Szeged 12 (1950), pp. 30-37.