Related papers: A note on a hypergeometric transformation formula …
We briefly sketch a proof concerning the structure of the all-order epsilon-expansions of generalized hypergeometric functions with special sets of parameters.
We study metric transformations including not just the field strength tensor of a $U(1)$ gauge field, but also its dual tensor. We first consider an arbitrary symmetric matrix built up with these two tensors in the metric transformation. It…
We establish a correspondence between one-parameter deformations of an affine Gorenstein toric pair $(X_P, \partial X_P)$, defined by a polytope $P$, and mutations of a Laurent polynomial $f$ with Newton polytope $\newt(f) = P$. For a…
We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…
After H\"older proved his classical theorem about the Gamma function, there has been a whole bunch of results showing that solutions to linear difference equations tend to be hypertranscendental i.e. they cannot be solution to an algebraic…
In 1981, Andrews gave a four-variable generalization of Ramanujan's ${_1\psi_1}$ summation formula. We establish a six-variable generalization of Andrews' identity according to the transformation formula for two ${_8\phi_7}$ series and…
We prove two transformations for the $p$-adic hypergeometric series which can be described as $p$-adic analogues of a Kummer's linear transformation and a transformation of Clausen. We first evaluate two character sums, and then relate them…
Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)} (r^2) r^{l} Y_{lm}(\vartheta,\varphi)$, $|m| \leq l < n \in \mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre…
We discuss the spectral decomposition of the hypergeometric differential operators on the line $\mathrm{Re}\, z=1/2$. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal…
We obtain a formula which reduces the evaluation of a $_2\psi_2$ series to two $_2\phi_1$ series. In some sense, this identity may be considered as a companion of Slater's formulas. We also find that a two-term ${}_2\psi_2$ summation…
Guillera has introduced remarkable series expansions for $\frac{1}{\pi^2}$ of convergence rates $-\frac{1}{1024}$ and $-\frac{1}{4}$ via the Wilf-Zeilberger method. Through an acceleration method based on Zeilberger's algorithm and related…
We describe a new realization of supersymmetry, called scalar supersymmetry, acting in spaces of differential forms (bi-spinors), where transformation parameters are Lorentz scalars instead of spinors. The realization is related but is not…
In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$,…
Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical…
A proof of an unusual summation formula for a basic hypergeometric series associated to the affine root system $\tilde A_n$ that was conjectured by Warnaar is given. It makes use of Milne's $A_n$ extension of Watson's transformation,…
We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.
A parameterization is described for quantifying translational motion of a point in three-dimensional Euclidean space. The parameterization is similar to well-known parameterizations such as spherical coordinates in that both position and…
The Gauss hypergeometric functions 2F1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers. It is shown that in the case of integer and/or…
We derive hypergeometric formulas for Euler's constant, gamma. A "by-product" of Thomae's transformation is an infinite product for e^gamma involving the binomial coefficients. Alternate, non-hypergeometric proofs use a double integral for…
We derive the Smarr formula for a five-dimensional spacetime which has a magnetic "bolt" in its center and is asymptotically R^(3,1) x S^1. Supersymmetry - and so the BPS-bound - is broken by the holonomy. We show how each topological…