query: smooth $C^\infty$ anywhere but analytical $C^{\omega}$ nowhere function
positive_passages.docid: 155871
positive_passages.text: Is it possible for a function to be smooth everywhere, analytic nowhere, yet Taylor series at any point converges in a nonzero radius?
negative_passages.docid: 125615
negative_passages.text: Defining the derivative without limits
negative_passages.docid: 79307
negative_passages.text: How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
negative_passages.docid: 109732
negative_passages.text: Nowhere continuous function limit
negative_passages.docid: 106531
negative_passages.text: A Fourier transform of a continuous $L^1$ function
negative_passages.docid: 108997
negative_passages.text: Continuous functions that attain local extrema at every point
negative_passages.docid: 71140
negative_passages.text: Pointwise limit of the sequence of continuously differentiable functions defined inductively.
negative_passages.docid: 105207
negative_passages.text: function with isolated singularity on the unit circle and coefficients of its taylor expansion
negative_passages.docid: 6417
negative_passages.text: Can a function be differentiable at the end points of its (closed interval) domain?
negative_passages.docid: 48246
negative_passages.text: Approximation of Riemann integrable function with a continuous function
negative_passages.docid: 37303
negative_passages.text: Differential of a smooth function
negative_passages.docid: 13732
negative_passages.text: $||f||_p\to ||f||_\infty$ under general assumptions
negative_passages.docid: 83517
negative_passages.text: Taylor series of Infinitely differentiable function with nonnegative derivatives
negative_passages.docid: 115878
negative_passages.text: Continuous unbounded but integrable functions
negative_passages.docid: 17223
negative_passages.text: Continuity of an inverse function.
negative_passages.docid: 74339
negative_passages.text: Integrable function whose Fourier transform is not integrable
negative_passages.docid: 100436
negative_passages.text: Examples of nowhere continuous functions