Inverse Formulas for the Fourier Coefficients of Meromorphic Functions in a Half-Plane

Quadrature formulas for Fourier coefficients

Meromorphic functions with positive coefficients

for some α (0≤α< 1). We say that f(z) is in the class ∑C(α) of such functions. The class ∑∗(α) and various other subclasses of ∑ have been studied rather extensively by Nehari and Netanyahu [9], Clunie [4], Pommerenke [11, 12], Miller [7], Royster [13], and others (cf., e.g., Bajpai [2], Goel and Sohi [6], Mogra et al. [8], Uralegaddi and Ganigi [15], Cho et al. [3], Aouf [1], and Uralegaddi an...

A special subspace of weighted spaces of holomorphic functions on the upper half plane

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry

We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a planewave background, for any value of the mass parameter μ. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We ...

Formulas for the Fourier Coefficients of Some Genus Zero Modular Functions

Kaneko gave a closed formula for the Fourier coefficients of the elliptic modular function j (τ ) expressed in terms of traces of singular moduli. We give analogues of his formula in higher-level cases.