Related papers: Uniform Asymptotic Expansion for the Incomplete Be…
Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between the logarithmic and psi functions, J. Comput. Appl. Math., vol. 361, pp. 366--371 (2019); available online at…
We consider the asymptotics of the partition function of the extended Gross-Witten-Wadia unitary matrix model by introducing an extra logarithmic term in the potential. The partition function can be written as a Toeplitz determinant with…
Let $p(n)$ denote the partition function. In this paper our main goal is to derive an asymptotic expansion up to order $N$ (for any fixed positive integer $N$) along with estimates for error bounds for the shifted quotient of the partition…
We establish sharp inequalities involving the incomplete Beta and Gamma functions. These inequalities arise in the approximation of generalized Bernstein functions by higher order Thorin-Bernstein functions. Furthermore, new properties of a…
We present a simple result that allows us to evaluate the asymptotic order of the remainder of a partial asymptotic expansion of the quantile function $h(u)$ as $u\to 0^+$ or $1^-$. This is focussed on important univariate distributions…
The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in…
We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one. We prove the existence of the full asymptotic expansions of these spherical integrals and derive the first and the second term in…
In this paper we prove that, for asymptotically bounded holomorphic functions defined in a polysector in ${\mathbb C}^n$, the existence of a strong asymptotic expansion in Majima's sense following a single multidirection towards the vertex…
In a previous work [J. Math. Phys. {\bf 35} (1994), 2539--2551], generalized hypergeometric functions have been used to a give a rigorous derivation of the large $s$ asymptotic form of the general $\beta > 0$ gap probability $E_\beta^{\rm…
We examine the sum of modified Bessel functions with argument depending non-linearly on the summation index given by \[S_{\nu,p}(a)=\sum_{n\geq 1} (an^p/2)^{-\nu} K_\nu(an^p)\qquad (a>0,\ 0\leq\nu<1)\] as the parameter $a\to 0+$, where $p$…
We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…
Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function $K_{i\tau}(x)$. The results can be applied, for instance, to study the summability of the divergent…
The results of part I (hep-ph/9612284) are used to obtain full asymptotic expansions of Feynman diagrams renormalized within the MS-scheme in the regimes when some of the masses and external momenta are large with respect to the others. The…
We introduce completely monotonic functions of order $r>0$ and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic functions of any…
We obtain structural theorems for the so-called S-asymptotic and quasiasymptotic boundedness of ultradistributions. Using these results, we then analyze the moment asymptotic expansion (MAE), providing a full characterization of those…
We study some series expansions for the Lambert $W$ function. We show that known asymptotic series converge in both real and complex domains. We establish the precise domains of convergence and other properties of the series, including…
We investigate the asymptotic expansion of integrals analogous to Ball's integral \[\int_0^\infty \left(\frac{\Gamma(1+\nu)|J_\nu(x)|}{(x/2)^\nu}\right)^{\!n}dx\] for large $n$ in which the Bessel function $J_\nu(x)$ is replaced by the…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In a previous paper L\'opez and Temme (1999) these polynomials have been considered for large…
In this article, we define a special function called the Bigamma function. It provides a generalization of Euler's gamma function. Several algebraic properties of this new function are studied. In particular, results linking this new…