We study unilateral series in a single variable q where its exponent is an unbounded increasing function, and the coefficients are periodic. Such series converge inside the unit disk. Quadratic polynomials in the exponent correspond to partial theta series. We compute limits of those series as the variable tends radially to a root of unity. The proofs use ideas from the q-integral and are elementary
In this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we esta...
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for ...
Following on from our recent investigation of series and products using the Euler–Maclaurin formula,...
We study unilateral series in a single variable q where its exponent is an unbounded increasing func...
We study unilateral series in a single variable q where its exponent is an unbounded increasing func...
The bivariate series $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ defines a {\em partial thet...
In previous work, the authors discovered new examples of q-hypergeometric series related to the arit...
AbstractThere is increasing interest inq-series with |q|=1. In analysis of these, all important role...
We study higher uniformity properties of the M\"obius function $\mu$, the von Mangoldt function $\La...
The purpose of this article is to define some intermediate q-Lauricella functions, to find convergen...
The purpose of this article is to define some intermediate q-Lauricella functions, to find convergen...
AbstractIn this paper the authors study “truncated” quadrature rules based on the zeros of Generaliz...
AbstractIt is shown how two doubly infinite sets of series involving π may be obtained using closure...
AbstractDixon’s classical summation theorem on F23(1)-series is reformulated as an equation of forma...
Derivative-matching approximations are constructed as power series built from functions. The method ...
In this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we esta...
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for ...
Following on from our recent investigation of series and products using the Euler–Maclaurin formula,...
We study unilateral series in a single variable q where its exponent is an unbounded increasing func...
We study unilateral series in a single variable q where its exponent is an unbounded increasing func...
The bivariate series $\theta (q,x):=\sum _{j=0}^{\infty}q^{j(j+1)/2}x^j$ defines a {\em partial thet...
In previous work, the authors discovered new examples of q-hypergeometric series related to the arit...
AbstractThere is increasing interest inq-series with |q|=1. In analysis of these, all important role...
We study higher uniformity properties of the M\"obius function $\mu$, the von Mangoldt function $\La...
The purpose of this article is to define some intermediate q-Lauricella functions, to find convergen...
The purpose of this article is to define some intermediate q-Lauricella functions, to find convergen...
AbstractIn this paper the authors study “truncated” quadrature rules based on the zeros of Generaliz...
AbstractIt is shown how two doubly infinite sets of series involving π may be obtained using closure...
AbstractDixon’s classical summation theorem on F23(1)-series is reformulated as an equation of forma...
Derivative-matching approximations are constructed as power series built from functions. The method ...
In this paper, by using the Bernoulli numbers and the exponential complete Bell polynomials, we esta...
We investigate infinite families of integral quadratic polynomials {fk (X)} k∈N and show that, for ...
Following on from our recent investigation of series and products using the Euler–Maclaurin formula,...
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