We consider the long time dependence for the moments of displacement <|r|(q)> of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find <|r|(q)> approximately t(gamma(q)) (up to factors of ln t). The time exponent, gamma(q), is piecewise linear and equal to q/2 for q<2 and q-1 for q>2. We discuss the lack of dependence of this res...

Abstract In the expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, the author looks back and analyses some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio...

Abstract. In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, the complete monotonicity of several functions involving ratios of two gamma or q-gamma functions, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions, some new bounds for the ratio of two ...

In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies $a_0(z)=1$. In this paper, we prove Becker's conjecture in the best-possible form; we show that the rational function $R(z)$ can be...

Abstract. Algorithms for the numerical evaluation of the incomplete gamma function ratios P (a, x) = γ(a, x)/Γ(a) and Q(a, x) = Γ(a, x)/Γ(a) are described for positive values of a and x. Also, inversion methods are given for solving the equations P (a, x) = p, Q(a, x) = q, with 0 < p, q < 1. Both the direct computation and the inversion of the incomplete gamma function ratios are used in many p...

Charge movement was measured in frog cut twitch fibers with the double Vaseline-gap technique. Steady-state inactivation of charge movement was studied by changing the holding potential from -90 mV to a level ranging from -70 to -30 mV. Q beta and Q gamma at each holding potential were separated by fitting the Q-V plot with a sum of two Boltzmann distribution functions. At -70 mV Q beta and Q g...

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Zp of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acqu...

We investigate the properties of algebraic gamma monomials— that is, algebraic numbers which are expressible as monomials in special values of the classical gamma function. Recently Anderson has constructed a double complex SK, to compute H∗(±,U), where U is the universal ordinary distribution. We use the double complex to deduce explicit formulae for algebraic gamma monomials. We provide simpl...