TY - JOUR
T1 - q-Analogs of identities involving harmonic numbers and binomial coefficients
AU - Mansour, Toufik
AU - Shattuck, Mark
AU - Song, Chunwei
PY - 2012/1/1
Y1 - 2012/1/1
N2 - Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q-analogs of a fair number of the identities appearing in [D. McCarthy, Integers 11, No. 6, 801–809 (2011; Zbl 1234.05039)] and [H. Prodinger, Integers 8, No. 1, Article A10, 8 p., electronic only (2008; Zbl 1162.05004)] by making use of q-partial fractions.
AB - Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q-analogs of a fair number of the identities appearing in [D. McCarthy, Integers 11, No. 6, 801–809 (2011; Zbl 1234.05039)] and [H. Prodinger, Integers 8, No. 1, Article A10, 8 p., electronic only (2008; Zbl 1162.05004)] by making use of q-partial fractions.
M3 - מאמר
SN - 1932-9466
VL - 7
SP - 22
EP - 36
JO - Applications and Applied Mathematics: An International Journal
JF - Applications and Applied Mathematics: An International Journal
IS - 1
ER -