ON GENERALIZATION OF WEIERSTRASS APPROXIMATION THEOREM FOR A GENERAL CLASS OF POLYNOMIALS AND GENERATING FUNCTIONS

Yıl 2016, Cilt: 6 Sayı: 1, 47 - 53, 01.06.2016

H. Kumar M. A. Pathan

Öz

Here, in this work we present a generalization of theWeierstrass ApproximationTheorem for a general class of polynomials. Then we generalize it for two variablecontinuous function F x; t and prove that on a rectangle [a; b]  -1; 1 ; a  x b; jtj

Anahtar Kelimeler

Weierstrass Approximation Theorem, Bernstein Approximation theorem, generalization of Weierstrass Approximation Theorem, generating functions.

Kaynakça

• Brown,J.W., (1969), New generating functions for classical polynomials, Proc. Amer. Math. Soc. 21, pp. 263-268.
• Estep,D., (2002), Practical Analysis in One Variable, Spriger, http://www.springer.com/978-0–387- 95484-4
• Rainville,E.D., (1960), Special Functions, Macmillan, New York; Reprinted by Chelsea Publ. Co., Bronx, New York.
• Schep,A.R., (2007), Weierstrass’ Proof of The Weierstrass Approximation Theorem, published in the site: www.math.sc.edu/˜schep/weierstrass.pdf
• Weierstrass,K., (1885), Uber die analytische Darstellbarkeit sogenannter willk, Urlicher Functionen einer reellen Ver, anderlichen, Verl. D. Kgl. Akad. D. Wiss. Berlin 2, pp. 633-639.