4 papers
math.CA2026
A further q-analogue of Gosper's strange series
John M. Campbell, Yuka Yamaguchi
Recently, the second author [Ramanujan J. 2026] introduced and proved a -series identity that appears to provide the first known -analogue of an evaluation for a ${}_{2}F_{1}…
math.CA2025
Basic hypergeometric identities derived from three-term relations
Yuka Yamaguchi
In 2015, Ebisu presented a new method for finding hypergeometric identities based on three-term relations for the hypergeometric series. By using this method, he der…
math.CA2025
Symmetries of coefficients of three-term relations for basic hypergeometric series
Yuka Yamaguchi
Any three basic hypergeometric series whose respective parameters and a variable are shifted by integer powers of are linearly related with coeffic…
math.CA2025
A -analogue of Gosper's strange evaluation of the hypergeometric series
Yuka Yamaguchi
In 1977, Gosper conjectured many strange evaluations of hypergeometric series. One of them is a -series identity with two free parameters, which was proved by Ebisu (2…