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Journal of Difference Equations and Applications, ISSN 1023-6198, 03/2018, Volume 24, Issue 3, pp. 438 - 451
In 2003, Rodriguez-Villegas conjectured four supercongruences on the truncated hypergeometric series for certain modular K3 surfaces, which were gradually... 
33B15 | p-adic Gamma functions | 11S80 | Secondary: 33C20 | Supercongruences | truncated hypergeometric series | Primary: 11A07
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2017, Volume 96, Issue 1, pp. 14 - 23
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2017, Volume 72, Issue 4, pp. 2057 - 2066
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2018, Volume 467, Issue 1, pp. 15 - 25
In 2006, Kimoto and Wakayama discussed one kind of Apéry-like numbers which occurs in a representation of the special value of the spectral zeta function, and... 
Apéry-like number | Spectral zeta function | Bernoulli number | Supercongruence | MATHEMATICS | MATHEMATICS, APPLIED | APERY-LIKE NUMBERS | Apery-like number | CONGRUENCES
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2017, Volume 72, Issue 4, pp. 2057 - 2066
Using an identity due to Gessel and Stanton and some properties of the p-adic Gamma function, we establish a p-adic supercongruence for truncated... 
Primary 11A07 | hypergeometric series | Secondary 33C20 | Supercongruences | Mathematics, general | Mathematics | p -adic Gamma functions
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2017, Volume 72, Issue 4, p. 2057
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00025-017-0744-y Using an... 
Information science
Journal Article
Journal of Symbolic Computation, ISSN 0747-7171, 07/2019, Volume 93, pp. 221 - 229
Using the software package developed by Schneider, we automatically discover and prove some combinatorial identities involving harmonic numbers, from which we... 
Combinatorial identities | Euler numbers | Harmonic numbers | Supercongruences | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 08/2018, Volume 24, Issue 8, pp. 1368 - 1373
We give q-analogues of the following two Ramanujan-type formulas for : Our proof is based on two q-WZ pairs found by the first author in his earlier work. 
Ramanujan | 05A10 | q-WZ pair | supercongruences | cyclotomic polynomial | 11B65 | 33D15
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 11/2019, pp. 1 - 11
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2019, Volume 471, Issue 1-2, pp. 613 - 622
In 1997, Van Hamme conjectured 13 Ramanujan-type supercongruences labeled (A.2)–(M.2). Using some combinatorial identities discovered by , we extend (A.2) and... 
p-adic Gamma functions | Hypergeometric series | Supercongruences | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 07/2019, pp. 1 - 8
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 08/2018, Volume 24, Issue 8, p. 1368
We give q-analogues of the following two Ramanujan-type formulas for [Formula omitted.] : [Formula omitted.] Our proof is based on two q-WZ pairs found by the... 
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 08/2018, Volume 98, Issue 1, pp. 27 - 37
We establish some supercongruences for the truncated F-2(1) and F-3(2) hypergeometric series involving the p-adic gamma functions. Some of these results extend... 
supercongruences | truncated hypergeometric series | p-adic gamma functions | LEGENDRE POLYNOMIALS | MATHEMATICS | PRODUCTS | BINOMIAL COEFFICIENTS | HYPERGEOMETRIC-SERIES
Journal Article
by Liu, JC
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2017, Volume 47, Issue 8, pp. 2723 - 2730
We obtain three finite generalizations of Gauss's square exponent identity. For example, we prove that, for any non-negative integer m, Sigma(m)(k=-m)(-1)(k)... 
MATHEMATICS | pentagonal number theorem | q-binomial coefficients | PROOFS | ANALOGS | Gauss's identity
Journal Article
by Liu, JC
COLLOQUIUM MATHEMATICUM, ISSN 0010-1354, 2019, Volume 158, Issue 2, pp. 255 - 263
By using some combinatorial identities and supercongruences due to Van Hamme and Tauraso, we establish two supercongruences on the truncated Appell series F-1... 
MATHEMATICS | supercongruences | p-adic Gamma functions | truncated Appell series | NUMBERS | CONJECTURE
Journal Article
by Liu, JC
CZECHOSLOVAK MATHEMATICAL JOURNAL, ISSN 0011-4642, 06/2017, Volume 67, Issue 2, pp. 525 - 531
Euler's pentagonal number theorem was a spectacular achievement at the time of its discovery, and is still considered to be a beautiful result in number theory... 
MATHEMATICS | pentagonal number theorem | q-binomial coefficient | q-binomial theorem | Information science
Journal Article
Results in Mathematics, ISSN 1422-6383, 12/2018, Volume 73, Issue 4, pp. 1 - 8
In this paper, we prove two congruences on the double sums of the super Catalan numbers (named by Gessel), which were recently conjectured by Apagodu. 
11A07 | Congruences | 05A10 | Mathematics, general | 05A19 | super Catalan numbers | Mathematics | Zeilberger’s algorithm | MATHEMATICS | MATHEMATICS, APPLIED | Zeilberger's algorithm | BINOMIAL COEFFICIENTS
Journal Article
Journal of Difference Equations and Applications, ISSN 1023-6198, 03/2018, Volume 24, Issue 3, pp. 438 - 451
In 2003, Rodriguez-Villegas conjectured four supercongruences on the truncated [Formula omitted.] hypergeometric series for certain modular K3 surfaces, which... 
p-adic Gamma functions | truncated hypergeometric series | Supercongruences | Combinatorial analysis
Journal Article
Journal of Number Theory, ISSN 0022-314X, 11/2017, Volume 180, pp. 566 - 572
By using the Rodriguez-Villegas–Mortenson supercongruences, we prove four supercongruences on sums involving binomial coefficients, which were originally... 
Delannoy number | Supercongruences | Legendre symbol | Zeilberger algorithm | MATHEMATICS | DELANNOY NUMBERS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 11/2016, Volume 168, pp. 117 - 127
The Delannoy numbers and Schröder numbers are given by respectively. Let be a prime. We mainly prove that where is the -th Bernoulli number and these are the... 
Delannoy numbers | Schröder numbers | Bernoulli numbers | Supercongruence | POLYNOMIALS | MATHEMATICS | Schroder numbers | CONGRUENCES
Journal Article
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