Some q-supercongruences from squares of basic hypergeometric series

被引：2

作者：

Song, Hanfei ^{[1
]}

Wang, Chun ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2024年 / 118卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Basic hypergeometric series; q-supercongruences; cyclotomic polynomial; creative microscoping; the Chinese remainder theorem; KANTOROVICH-TYPE OPERATORS; APPROXIMATION;

D O I：

10.1007/s13398-023-01534-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Inspired by the recent work of El Bachraoui and Guo-Li, we establish several q-supercongruences on the truncated forms of squares of basic hypergeometric series modulo the cube and the fourth power of a cyclotomic polynomial. Our proofs heavily rely on the creative microscoping method devised by Guo and Zudilin, a lemma due to El Bachraoui and the Chinese remainder theorem for coprime polynomials.

引用

页数：15

共 73 条

[61]

Mamedov R. G., 1991, MELLIN TRANSFORM APP, V273

[62]

Miclaus D., 2013, CREAT MATH INFORM, V22, P73, DOI 10.37193/CMI.2013.01.09

[63] Approximation Process Based on Parametric Generalization of Schurer-Kantorovich Operators and their Bivariate Form [J].

Nasiruzzaman, Md ;

Srivastava, H. M. ;

Mohiuddine, S. A. .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2023, 93 (01) :31-41

[64] Two q-supercongruences from Watson's transformation [J].

Ni, He-Xia ;

Wang, Li-Yuan .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2022, 116 (01)

[65] Statistical approximation results for Kantorovich-type operators involving some special polynomials [J].

Ozarslan, M. Ali ;

Duman, Oktay ;

Srivastava, H. M. .

MATHEMATICAL AND COMPUTER MODELLING, 2008, 48 (3-4) :388-401

[66] Some approximation results involving the q-Szasz-Mirakjan-Kantorovich type operators via Dunkl's generalization [J].

Srivastava, H. M. ;

Mursaleen, M. ;

Alotaibi, Abdullah M. ;

Nasiruzzaman, Md. ;

Al-Abied, A. A. H. .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (15) :5437-5452

[67] On the supercongruence conjectures of van Hamme [J].

Swisher, Holly .

RESEARCH IN THE MATHEMATICAL SCIENCES, 2015, 2 (01)

[68] A new q-supercongruence modulo the fourth power of a cyclotomic polynomial [J].

Tang, Na .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2023, 117 (03)

[69] q-Supercongruences on Triple and Quadruple Sums [J].

Wang, Xiaoxia ;

Xu, Chang .

RESULTS IN MATHEMATICS, 2023, 78 (01)

[70] A q-ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE [J].

Wang, Xiaoxia ;

Yue, Mingbing .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2021, 103 (02) :303-310

← 1 2 3 4 5 6 7 8 →