New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
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Qiuxia Hu
Abstract
In terms of a very-well-poised 6ϕ5 summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new q-supercongruences for truncated basic hypergeometric series. One of these results is a new q-analogue of the (F.2) supercongruence of Van Hamme.
This work is supported by the National Natural Science Foundation of China (Nos. 12101287, 12271234) and International science and technology cooperation project of Henan Province (No. 242102520002).
Acknowledgement
The author thanks the anonymous referees for careful readings of a previous version of this paper.
Communicated by Marco Cantarini
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- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
- On asymptotics for lacunary partition functions
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- Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
- Approximation theorems via Pp-statistical convergence on weighted spaces
- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
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- Influence of ideals in compactifications
- On the functions ωf and Ωf
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