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Background This question is related to this one, in the sense that, as the previous one, it originates from my efforts to extend an estimate on the remainder of a power series on a non necessarily ...

Notation and premises. Here it is a list of notations more or less explicitly used in the question: If $z\in\Bbb C$ then $z = re(t)$ where $r\in \Bbb R_{\ge 0}$, $t\in [0,1]$ and $e(t)\triangleq \exp(...

$t^n=a$, we get one solution to the equation: $$t=e^{\frac{1}{n}\int^a_1 \frac{1}{x}}$$ generalizing this result by replacing the exponential with an elliptic modular function and the integral with ...

there are examples of lacunary functions with natural boundary that do not satisfy Fabry or Hadamard gap theorem condition.I want to know more examples of those functions,the more the better,...