The Journal of the Indian Mathematical Society

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The Derivatives of Certain Functions


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1 State College, Pa, United States
     

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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 ex-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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  • The Derivatives of Certain Functions

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Authors

I. M. Sheffer
State College, Pa, United States

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 ex-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.