Mean Value Theorems for Special Polynomials

Abstract

In this paper, we derive and analyze mean value theorems for several important classes of special polynomials, including
Chebyshev, Hermite, and Bessel polynomials. These theorems provide valuable insights into the average behavior of these
polynomials over specific intervals or domains. By utilizing orthogonality properties and recurrence relations, we explore
the implications of the mean value results, supported by numerical examples. The results have significant applications in
numerical analysis, approximation theory, and mathematical physics.