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Let's assume $x\in[0,1]$, and restrict all functions of $x$ that we consider to this domain. Consider a sequence $\mathcal S_n$ of sets of functions, where $n^{\text{th}}$ element is the set of all ...

Define an operator $\mathop{\vec{\bigcup}}$ as follows: Definition. Whenever $A$ is an $I$-indexed family of sets, where $I$ is a totally-ordered set, we have $$\mathop{\vec{\bigcup}}_{i \in I} A_i ...

I would like to know the asymptotic expansion of the sequence of positive numbers given by $$I_{n}:=-\int_{0}^{1}\frac{n^{x-1}}{\Gamma(x-1)}dx,$$ for $n\rightarrow\infty$. One can easily derive an ...