Some Applications of the $(f,g)$-Inversion
Received:September 07, 2018  Revised:May 18, 2019
Key Word: Matrix inversion   $(f,g)$-Inversion   Hypergeometric series   Basic hypergeometric series   $q$-Differential operator  
Fund ProjectL:National Natural Science Foundation of China (grants 11471244 and 11771330)
Author NameAffiliationE-mail
Yan-Ping Mu College of Science, Tianjin University of Technology yanping.mu@gmail.com 
Xiaozhou Tong College of Science, Tianjin University of Technology  
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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.
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