The Journal of the Indian Mathematical Society

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Weirstrass' Non-Differentiable Function


     

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The best condition that has been given hitherto for the differentiability of f(x) = ∞Σ0 an cos bn πX is that ab > 1 + 3π /2(1 - a), where 0 < a < 1 and b an odd integer-a condition due to Bromwich. The case when b is even has been mentioned by Hardy in the T.A.M.S. (1916) in which he gives a condition given by Dini.
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  • Weirstrass' Non-Differentiable Function

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Abstract


The best condition that has been given hitherto for the differentiability of f(x) = ∞Σ0 an cos bn πX is that ab > 1 + 3π /2(1 - a), where 0 < a < 1 and b an odd integer-a condition due to Bromwich. The case when b is even has been mentioned by Hardy in the T.A.M.S. (1916) in which he gives a condition given by Dini.