query: Is the gamma function $\Gamma(n+1)$ the only continuous function and defined derivative with the same recursive definition as of $n!$ for $n>-1$?
positive_passages.docid: 25729
positive_passages.text: Why is Euler's Gamma function the "best" extension of the factorial function to the reals?
negative_passages.docid: 43956
negative_passages.text: Differentiating $f(x)^{g(x)}$
negative_passages.docid: 119869
negative_passages.text: Entire function and the series of its successive derivatives
negative_passages.docid: 49587
negative_passages.text: Does a differentiable everywhere function have a continuous derivative?
negative_passages.docid: 68484
negative_passages.text: Revision of Borel-Cantelli, $(X_n)_{n \geq 1}$ sqn of $\geq 0$ identical RVs with $E(X) < \infty$ then $X_n/n \to 0$ a.s., are my arguments correct?
negative_passages.docid: 145233
negative_passages.text: How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
negative_passages.docid: 113740
negative_passages.text: Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
negative_passages.docid: 48867
negative_passages.text: why all constant functions are continuous.$?$
negative_passages.docid: 28315
negative_passages.text: Monotone functions and non-vanishing of derivative
negative_passages.docid: 141945
negative_passages.text: Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
negative_passages.docid: 41557
negative_passages.text: Most general $A \subseteq \mathbb R$ to define derivative of $f: A \to \mathbb R$?
negative_passages.docid: 118048
negative_passages.text: Can a function with just one point in its domain be continuous?
negative_passages.docid: 139720
negative_passages.text: Are all continuous one one functions differentiable?
negative_passages.docid: 22916
negative_passages.text: Derivative of sigmoid function $\sigma (x) = \frac{1}{1+e^{-x}}$
negative_passages.docid: 66560
negative_passages.text: Is a differentiable function always continuous?
negative_passages.docid: 24306
negative_passages.text: Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
negative_passages.docid: 68752
negative_passages.text: A few questions about infinite derivative.