Related papers: Truncated Hypergeometric Functions and Discretized…
We express some general type of infinite series such as $$ \sum^\infty_{n=1}\frac{F(H_n^{(m)}(z),H_n^{(2m)}(z),\ldots,H_n^{(\ell m)}(z))} {(n+z)^{s_1}(n+1+z)^{s_2}\cdots (n+k-1+z)^{s_k}}, $$ where $F(x_1,\ldots,x_\ell)\in\mathbb…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
By dividing hypergeometric series representations of the inverse sine by sin^-1 (x) and integrating, new double series representations of integers and constants arise. Binomial coefficients and the sine integral are thus combined in double…
We prove a master theorem for hypergeometric functions of Karlsson-Minton type, stating that a very general multilateral U(n) Karlsson-Minton type hypergeometric series may be reduced to a finite sum. This identity contains the…
Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential properties on the period is introduced. Finite Fourier…
Motivated by recent work of George Andrews and Mircea Merca on the expansion of the quotient of the truncation of Euler's pentagonal number series by the complete series, we provide similar expansion results for averages involving…
Square grid circle patterns with prescribed intersection angles, mimicking holomorphic maps z^a and log(z) are studied. It is shown that the corresponding circle patterns are imbedded and described by special separatrix solutions of…
We introduce the unified double zeta function of Mordell--Tornheim type and compute its values at non-positive integer points. We then discuss a possible generalization of the Kaneko--Zagier conjecture for all integer points.
We introduce new hypergeometric series expansions of the solutions to the general Heun equation. The form of the Gauss hypergeometric functions used as expansion function differs from that used before. We derive three such expansions and…
We show various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.
We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
We study consistent truncations in the framework of Exceptional Generalised Geometry. We classify the 4-dimensional gauged supergravities that can be obtained as a consistent truncation of 10/11-dimensional supergravity. Any truncation is…
In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…
Hypergeometric functions over finite fields were introduced by Greene in the 1980s as a finite field analogue of classical hypergeometric series. These functions, and their generalizations, naturally lend themselves to, and have been widely…
The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series. As a prior research, the second-named author considered double analogues of Eisenstein series and expressed them as…
In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums…
In the article, some Huygens and Wilker type inequalities involving trigonometric and hyperbolic functions are refined and sharpened.