Open Accessq-binomial formulae of Dixon`s type and the Fibonomial sums
Author(s) -
Wenchang Chu,
Emrah Kılıç
Publication year - 2020
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm190406016c
Subject(s) - mathematics , gaussian binomial coefficient , binomial coefficient , binomial theorem , binomial approximation , series (stratigraphy) , central binomial coefficient , base (topology) , binomial (polynomial) , type (biology) , value (mathematics) , transformation (genetics) , pure mathematics , negative binomial distribution , discrete mathematics , mathematical analysis , statistics , paleontology , ecology , biochemistry , chemistry , gene , poisson distribution , biology
Cubic sums of the Gaussian q-binomial coefficients with certain weight functions will be evaluated in this paper. To realize this, we will derive two remarkable formulae by means of the Carlitz-Sears transformation on terminating well-poised q-series. As consequences, several summation formulae on Fibonomial coefficients are presented by specializing the value of base q in our q-series identities.