| Some Applications of the $(f,g)$-Inversion |
| Received:September 07, 2018 Revised:May 22, 2019 |
| Key Words:
matrix inversion $(f,g)$-inversion hypergeometric series basic hypergeometric series $q$-differential operator
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.\,11471244; 11771330). |
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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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