Results 131 to 140 of about 100,499 (167)

Summation Formulas on Harmonic Numbers and Five Central Binomial Coefficients

Mathematical Notes, 2023
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Li, Chunli, Chu, Wenchang
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INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS

International Journal of Number Theory, 2009
By means of two hypergeometric summation formulae, we establish two large classes of infinite series identities with harmonic numbers and central binomial coefficients. Up to now, these numerous formulae have hidden behind very few known identities of Apéry-like series for Riemann-zeta function, discovered mainly by Lehmer [14] and Elsner [12] as well ...
CHU, Wenchang, ZHENG D. Y.
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PROOF OF TWO CONJECTURES ON SUPERCONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS

Bulletin of the Australian Mathematical Society, 2020
In this note we use some $q$-congruences proved by the method of ‘creative microscoping’ to prove two conjectures on supercongruences involving central binomial coefficients. In particular, we confirm the $m=5$ case of Conjecture 1.1 of Guo [‘Some generalizations of a supercongruence of Van Hamme’, Integral Transforms Spec. Funct.28 (2017), 888–899].
CHENG-YANG GU, VICTOR J. W. GUO
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Interesting Series Involving the Central Binomial Coefficient

The American Mathematical Monthly, 1985
(1985). Interesting Series Involving the Central Binomial Coefficient. The American Mathematical Monthly: Vol. 92, No. 7, pp. 449-457.
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Wallis's Product and the Central Binomial Coefficient

The American Mathematical Monthly, 2015
(2015). Wallis's Product and the Central Binomial Coefficient. The American Mathematical Monthly: Vol. 122, No. 7, pp. 689-689.
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ON SOME CONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS

Bulletin of the Australian Mathematical Society
AbstractWe prove the following conjecture of Z.-W. Sun [‘On congruences related to central binomial coefficients’, J. Number Theory13(11) (2011), 2219–2238]. Let p be an odd prime. Then $$ \begin{align*} \sum_{k=1}^{p-1}\frac{\binom{2k}k}{k2^k}\equiv-\frac12H_{{(p-1)}/2}+\frac7{16}p^2B_{p-3}\pmod{p^3}, \end{align*} $$ where $H_n$ is the nth harmonic
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DIVISIBILITY OF CERTAIN SUMS INVOLVING CENTRAL q-BINOMIAL COEFFICIENTS

Rocky Mountain Journal of Mathematics
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Chen, Yifan, Wang, Xiaoxia
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Some congruences involving fourth powers of central q-binomial coefficients

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2019
AbstractWe prove some congruences on sums involving fourth powers of central q-binomial coefficients. As a conclusion, we confirm the following supercongruence observed by Long [Pacific J. Math. 249 (2011), 405–418]: $$\sum\limits_{k = 0}^{((p^r-1)/(2))} {\displaystyle{{4k + 1} \over {{256}^k}}} \left( \matrix{2k \cr k} \right)^4\equiv p^r\quad \left( {
Guo, Victor J. W., Wang, Su-Dan
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Number of divisors of the central binomial coefficient

Moscow University Mathematics Bulletin, 2013
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Series Involving Cubic Central Binomial Coefficients of Convergence Rate 1/64

Bulletin of the Malaysian Mathematical Sciences Society
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Chunli Li, Wenchang Chu
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