for orbitals ψ centered at places A, B, C and D. The Gauss Transformation Method has been shown to calculate the integral if the orbitals ψ are expanded in a basis of Gaussian Type Orbitals (GTO’s) [4]; this manuscript basically demonstrates how dealing with the quadratic forms in the exponentials directly also manages to reduce them to the omnipresent Confluent Hypergeometric Functions of the ...

— We draw up the list of Gauss hypergeometric differential equations having maximal unipotent monodromy at 0 whose associated mirror map has, up to a simple rescaling, integral Taylor coefficients at 0. We also prove that these equations are characterized by much weaker integrality properties (of p-adic integrality for infinitely many primes p in suitable arithmetic progressions). It turns out ...

Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

A fractional generalized pure birth process is studied based on the master equation approach. The exact analytic solution of the generating function of the probability density for the process is given in terms of the Gauss hypergeometric function. The expressions of moments are also obtained in an explicit form. The effects of fixed and distributed initial conditions are also elucidated. The ef...

Due to the isotropy of d-dimensional hyperspherical space, one expects there to exist a spherically symmetric fundamental solution for its corresponding Laplace–Beltrami operator. The R-radius hypersphere SR with R > 0, represents a Riemannian manifold with positive-constant sectional curvature. We obtain a spherically symmetric fundamental solution of Laplace’s equation on this manifold in ter...

A harmonic mapping is a univalent function of one complex variable. We define family mappings on the unit disk whose images are rotationally symmetric “rosettes” with n cusps or nodes, \(n\ge 3\). These analogous to n-cusped hypocycloid, but modified by Gauss hypergeometric factors, both in analytic and co-analytic parts. Relative rotations an angle \(\beta \) anti-analytic parts lead graphs th...

Generalised hypergeometric sheaves are rigid local systems on the punctured projective line with remarkable properties. Their study originated in seminal work of Riemann Euler–Gauss function and has blossomed into an active field connections to many areas mathematics. In this paper, we construct Hecke eigensheaves whose eigenvalues irreducible systems, thus confirming a central conjecture geo...

The main purpose of this paper is to compute all irreducible spherical functions on G = SL(2,C) of arbitrary type δ ∈ K̂, where K = SU(2). This is accomplished by associating to a spherical function Φ on G a matrix valued function H on the three dimensional hyperbolic space H = G/K. The entries of H are solutions of two coupled systems of ordinary differential equations. By an appropriate twisti...

Following a recent work of Dolan and Osborn, we consider superconformal indices of four dimensional N = 1 supersymmetric field theories related by an electric-magnetic duality with the SP (2N) gauge group and fixed rank flavour groups. For the SP (2) (or SU(2)) case with 8 flavours, the electric theory has index described by an elliptic analogue of the Gauss hypergeometric function constructed ...