The Journal of the Indian Mathematical Society

H. L. Krall ¹, I. M. Sheffer ¹

Affiliations
1 Department of Mathematics, Pennsylvania State University, University Park, (Penna) 16802, US

Abstract

It is shown that the classical set {cos nx, sin nx} is the only real trigonometric polynomial set that satisfies a linear differential equation of the form Σ̅ a_k (x)y^(k)_n(x) = λ_n y_n (x) where λ_n is a parameter and the i coefficients {a_k(x)} are independent of n.

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I. M. Sheffer ¹

Affiliations
1 State College, Pa, US

Abstract

It was shown by V. G. Iyer [3] that if f(x) is analytic on the closed interval [a, b], and if for some point x₀ ∈ [a, b] the sequence of derivatives f(ⁿ)(x₀) has a limit : fⁿ (x₀) ⃗ l, then f(ⁿ)(x) ⃗ l e^x-r° uniformly for x on [a, b]. Boas and Chandrasekharan [1], [2] reach the same conclusion with weaker assumptions on f(x). We propose to consider some extensions of this result of Iyer.

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