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math.CA2016
On a strange evaluation of the hypergeometric series by Gosper. II
Akihito Ebisu
There are many identities for the hypergeometric series presented in the article "Special values of the hypergeometric series" by Ebisu. In this note, we obtain a new hypergeometri…
math.CA2016
Special values of Gauss's hypergeometric series derived from Appell's series with closed forms
Akihito Ebisu
In a previous work ([Eb]), the author proposed a method employing contiguity relations to derive hypergeometric series in closed form. In [Eb], this method was used to derive Gauss…
math.CA2016
Three-Term Relations for 3F2(1)
Akihito Ebisu, Katsunori Iwasaki
For the hypergeometric function of unit argument 3F2(1) we prove the existence and uniqueness of three-term relations with arbitrary integer shifts. We show that not only the origi…