Limiting behaviour of a class of analytic functions for large arguments on the real axis

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Dated: 2 December 2016

This is not a physics essay but a mathematics one. It was more or less the conclusion of a discussion under what circumstances (if any) the fact that the limit of a continuous function is constant as its argument approaches infinity implies its derivative at infinity to vanish. Interestingly, this paper was visited only by a few for more than a year, but suddenly became my most-read essay of all so far, having several hundreds of reads! One definite answer that I gave was that if the limit of the derivative of the function discussed exists at infinity, then it must be zero. The essay, however, is about the question, whether bounded variation of the function considered is sufficient to make its derivative at infinity exist and vanish. I give a negative answer by counterexample. In fact, I consider a whole class of analytic functions, all of which have a constant limit at infinity. All except one are of bounded variation. For none of them, the limit of their derivative exists for x → ∞.

Limiting behaviour of a class of analytic functions for large arguments on the real axis, 02.12.2016

Next: Superluminal communication scheme wrong   Up: Introduction science education project    Previous: Derivation of the Schwarzschild geometry

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