We define the incomplete gamma function ratio for positive N by \begin{align*}\tag{1}P(N, b, X) &= \int^X_0 t^{N-1}e^{-bt} dt/ \int^\infty_0 t^{N-1}e^{-bt} dt \\ &\equiv \int^X_0 D(N, b, t) dt, ...

I'm afraid my math in this area is a bit deficient, but what I am trying to do is see if there's a way to simplify the function: but I never really learned how to manipulate factorials algebraically, ...

We prove among others results that the harmonic mean of Γq(ₓ) and Γq(1/ₓ) is greater than or equal to 1 for arbitrary x > 0, and q ∈ J where J is a subset of [0, +∞). Also, we prove that there is a ...

A new study in mice and rats found that restoring certain signals in a brain region that processes smells countered depression. Led by researchers from NYU Grossman School of Medicine and University ...

"It is larger than the size of most anything to which it might be compared." The universe's largest structure, the Hercules-Corona Borealis Great Wall, was already a challenge to explain with models ...