Some Applications of the $(f,g)$-Inversion
Received:September 07, 2018  Revised:May 22, 2019
Key Word: matrix inversion   $(f,g)$-inversion   hypergeometric series   basic hypergeometric series   $q$-differential operator  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.\,11471244; 11771330).
Author NameAffiliation
Yanping MU College of Science, Tianjin University of Technology, Tianjin 300384, P. R. China 
Xiaozhou TONG College of Science, Tianjin University of Technology, Tianjin 300384, P. R. China 
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Abstract:
      We present three kinds of applications of the $(f,g)$-inversion due to Ma. By taking explicit functions and sequences in the $(f,g)$-inversion, we derive identities involving hypergeometric series and harmonic numbers. Then we give several inversion relations involving $q$-hypergeometric terms. Finally, we combine the $(f,g)$-inversion and the $q$-differential operators to derive some $q$-series identities.
Citation:
DOI:10.3770/j.issn:2095-2651.2019.05.001
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