query: Why is the Gamma function $\Gamma$ used for interpolating factorials? Is it wrong to say that $(4.3)! = \Gamma(3.3)$?
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: 43499
negative_passages.text: Repeatedly taking differences on a polynomial yields the factorial of its degree?
negative_passages.docid: 46144
negative_passages.text: Understanding imaginary exponents
negative_passages.docid: 100801
negative_passages.text: A $\log \Gamma $ identity: Where does it come from?
negative_passages.docid: 143947
negative_passages.text: How to come up with the gamma function?
negative_passages.docid: 125966
negative_passages.text: Why there's a finite $\Gamma '$ such that $\Gamma ' \vDash \varphi$?
negative_passages.docid: 33585
negative_passages.text: Moment generating function of a gamma distribution
negative_passages.docid: 103628
negative_passages.text: Is the canonical parameter (and therefore the canonical link function) for a Gamma not unique?
negative_passages.docid: 66364
negative_passages.text: Why is $(\sqrt{2}+\sqrt{3})^{2008}$ so close to an integer?
negative_passages.docid: 66475
negative_passages.text: How can I prevent Overflow for the Gamma function?
negative_passages.docid: 7477
negative_passages.text: Why is the momentum of a particle $\gamma mv$?
negative_passages.docid: 99502
negative_passages.text: Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$
negative_passages.docid: 27969
negative_passages.text: Why does $\frac{1}{x} < 4$ have two answers?
negative_passages.docid: 56745
negative_passages.text: Why does this not work with an imaginary exponent?
negative_passages.docid: 158114
negative_passages.text: Representing the double factorial of LaguerreL[n, 1, x]/( (n + 1) LaguerreL[n, 0, x])
negative_passages.docid: 45280
negative_passages.text: Is there an Inverse Gamma $\Gamma^{-1} (z) $ function?
negative_passages.docid: 67322
negative_passages.text: evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$