MathDB
Miklos Schweitzer 1974_6

Source:

November 12, 2008
inductionfunctionlogarithmsintegrationlimitreal analysisreal analysis unsolved

Problem Statement

Let f(x)\equal{}\sum_{n\equal{}1}^{\infty} a_n/(x\plus{}n^2), \;(x \geq 0)\ , where \sum_{n\equal{}1}^{\infty} |a_n|n^{\minus{} \alpha} < \infty for some α>2 \alpha > 2. Let us assume that for some β>1/α \beta > 1/{\alpha}, we have f(x)\equal{}O(e^{\minus{}x^{\beta}}) as x→∞ x \rightarrow \infty. Prove that an a_n is identically 0 0. G. Halasz
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