Two $q$-analogues of Euler’s formula $\zeta (2)=\pi ^2/6$

DOI10.4064/cm7686-11-2018zbMath1437.05025arXiv1802.01473OpenAlexW2972151925MaRDI QIDQ5207303

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Publication date: 19 December 2019

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01473

zbMATH Keywords

zeta function\(q\)-analogueidentity

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) (zeta (s)) and (L(s, chi)) (11M06) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (7)

\(q\)-analogues of some series for powers of \(\pi\) ⋮ On two double series for \(\pi\) and their \(q\)-analogues ⋮ $q$-analogues of several $\pi $-formulas ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series: even powers ⋮ A \(q\)-analogue for Euler's evaluations of the Riemann zeta function ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ On decomposition of \(\theta_2^{2n}(\tau)\) as the sum of Eisenstein series and cusp forms

Cites Work

• On the representation of integers as sums of triangular numbers
• A \(q\)-analogue of the Bailey-Borwein-Bradley identity
• q-Analogues of two Ramanujan-type formulas for 1/π
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