q-Supercongruences from Gasper and Rahman's summation formula

نویسندگان

چکیده

In 2017, He (2017) [9] established two supercongruences on truncated hypergeometric series and further proposed related conjectures. Subsequently, Liu [11] extended He's formulas confirmed the second conjecture. However, first conjecture is still open up to now. With help of creative microscoping method Chinese remainder theorem for coprime polynomials, we derive several q-supercongruences modulo fourth fifth powers a cyclotomic polynomial from Gasper Rahman's summation formula basic series. As conclusions, more general form proved.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On q-summation and confluence

This paper is divided in two parts. In the first part we consider a convergent q-analog of the divergent Euler series, with q ∈ (0, 1), and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding q-difference equation. In the second part, we work under the assumptio...

متن کامل

SOME CURIOUS q-SUMMATION FORMULAE

We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Another consequence is a rather unusual summation formulae in which one side is an infinite basic-hyper...

متن کامل

On q-Operators and Summation of Some q-Series

Using Jackson's q-derivative and the q-Stirling numbers, we establish some transformation theorems leading to the values of some convergent q-series.

متن کامل

New Proofs of Some q-Summation and q-Transformation Formulas

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.

متن کامل

Euler Summation Formula for Path Integrals

We present and comment on some details of a new analytical method for systematic improvement of the convergence of path integrals of a generic N -fold discretized theory. The new methods represents a Euler summation formula for path integrals. Keeping the first p terms in this formula improves convergence of path integrals to the continuum limit to 1/N. We have given explicit calculations up to...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Advances in Applied Mathematics

سال: 2022

ISSN: ['1090-2074', '0196-8858']

DOI: https://doi.org/10.1016/j.aam.2022.102376