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.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2022
ISSN: ['1090-2074', '0196-8858']
DOI: https://doi.org/10.1016/j.aam.2022.102376