A new asymptotic expansion is derived for the incomplete beta function I(a, b, x), which is suitable for large a, small b and x > 0.5. This expansion is of the form I(a, b, x) ∼ Q(b,−γ log x) + Γ(a+ b) Γ(a)Γ(b) x ∞ ∑

We propose a generalization of Grunberg’s method of effective charges in which, starting with the effective charge for some dimensionless QCD observable dependent on the single energy scale Q, R(Q), we introduce an infinite set of auxiliary effective charges, each one describing the sub-asymptotic Qevolution of the immediately preceding effective charge. The corresponding infinite set of couple...

In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

We give a Wilsonian formulation of non-Abelian gauge theories explicitly consistent with axial gauge Ward identities. The issues of unitarity and dependence on the quantization direction are carefully investigated. A Wilsonian computation of the one-loop QCD beta function is performed. PACS: 11.10.Hi, 11.15.-q, 11.38.Bx.

Let $$T(q) = \sum\limits_{k 1}^\infty {d(k){q^k},\,\,\,\,\left| q \right| < 1,} $$ where d(k) denotes the number of positive divisors natural k. We present monotonicity properties functions defined in terms T. More specifically, we prove that $$H(q) T(q) - {{\log (1 q)} \over {\log (q)}}$$ is strictly increasing on (0, 1), while $$F(q) {{1 q} q}H(q)$$ decreasing 1). These results are then ap...

In this paper, we propose a new parametric distribution which called as the Beta Modified Weibull Power Series (BMWPS) distribution. This distribution is obtained by compounding Beta Modified Weibull (BMW) and power series distributions. BMWPS distribution contains, as special sub-models, such as Beta Modified Weibull Poisson (BMWP) distribution, Beta Modified Weibull Geometric (BMWG) distribut...

In this paper, our main focus is to define a new subfamily of q-analogue analytic functions associated with the q-cosine function. Furthermore, we investigate some useful results such as necessary and sufficient condition based on convolution idea, growth distortion bounds, closure theorem, convex combination, radii starlikeness, extreme point theorem partial sums for newly-defined class.