Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition inhomogeneous versions equations considered, case polynomial forcing terms. The involve exponential, Airy Scorer functions slowly varying analytic coefficient involving simple coefficients. approximations uniformly valid large values parameter unbounded real complex argument. ...

Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...

We prove solution uniqueness for the genus one Canham variational problem arising in shape prediction of biomembranes. The proof builds on a result Yu and Chen that reduces to proving positivity sequence defined by linear recurrence relation with polynomial coefficients. combine rigorous numeric analytic continuation D-finite functions classic bounds from singularity analysis derive an effectiv...

We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynom...

Abstract. Let P (z) and Q(y) be polynomials of the same degree k ≥ 1 in the complex variables z and y, respectively. In this extended abstract we study the non-linear functional equation P (z) = Q(y(z)), where y(z) is restricted to be analytic in a neighborhood of z = 0. We provide sufficient conditions to ensure that all the roots of Q(y) are contained within the range of y(z) as well as to ha...

where I is a finite set of distinct tuples (α0,α1, . . . ,αk) for which eachαi is a nonnegative integer, and the aᾱ are meromorphic functions in D = {z | |z| < 1}. For some index sets I, we determine conditions on aᾱ, whereby a meromorphic solution f of (1.1) in D will have finite order of growth as measured by the Ahlfors-Shimizu characteristic function. In [1], Bank investigated (1.1) where I...