Talk:Gamma function

Integrals

I prefer the form $\int dx\;f(x)$ (operator-like) instead of the form $\int f(x)dx$; both are correct; no need to change it the next time:D --ShinTakezou 20:01, 5 March 2009 (UTC)

Hmm, I never saw this form in mathematical literature. Technically, there is no any multiplication of f(x) by dx. You cannot commute them, if you meant that. And integral operator is not equal to definite integral. The definite integral using the integral operator would be sort of: ${\int f}\mid _{a}^{b}$. --Dmitry-kazakov 20:55, 5 March 2009 (UTC)

I did my math in my life, and I've seen it. Seen or not, there's a simple analogy between $\textstyle {\frac {d}{dx}}$ and $\textstyle \int dx$. Going into definite thing, there's no a rule stating that $\textstyle \int _{x_{0}}^{x_{1}}dxf(x)$ can't mean the integral of f(x) computed between x₀ and x₁; the analogy with derivative could be $\textstyle \left({\frac {d}{dx}}f(x)\right)_{x=x_{0}}$ (or any of the form you prefer to say the derivative of f(x) computed in x₀); no need for the integral to put limits "outside" the "operator boundary" like your attempt $\textstyle \left.\int f\right|_{a}^{b}$. More close analogy would be with the sum $\textstyle \sum _{i=1}^{N}f(x_{i})$ (the integral sign is nothing but an S). But this discussion is OT for RC. Mine was not an error, I will write it the same way for other "math" tasks; no need to fix it. --ShinTakezou 11:34, 6 March 2009 (UTC)

$\int dx\;f(x)$ is better, it makes more sense. I don't think there is anyone who has taken upper division undergraduate or graduate level math or physics courses who hasn't seen this notation. Though, that's far from a good argument for why this notation should be used. Chris Ferri 06:08, 21 September 2010 (UTC)

I do not think sense can be meaningfully quantified. That said, $\int dx\;f(x)$ means "the integral with respect to dx of f(x)" where $\int f(x)dx$ means "The integral of f(x) with respect to dx". They mean the same to someone that understands them both and the notation suggests possible variations, but... I am not sure that concepts of "sense" can even be partially ordered without contradicting other people's concepts of what does and does not make sense. --Rdm 16:41, 21 September 2010 (UTC)

Complex field

Actually Gamma is defined on complex numbers. Is the task about its real part only? --Dmitry-kazakov 22:25, 5 March 2009 (UTC)

Yes. Gamma can be defined on complex field, but the same works for real numbers (it is the opposite). The task asks only for the real one. --ShinTakezou 11:37, 6 March 2009 (UTC)