1 citations · 1 across the 8 of their papers we have counts for
10 papers
A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions
Akihito Ebisu, Yoshishige Haraoka, Masanobu Kaneko +3
A Fuchsian system of rank 8 in 3 variables with 4 parameters is presented. The singular locus consists of six planes and a cubic surface. The restriction of the system onto the int…
Contiguous Relations, Laplace's Methods and Continued Fractions for 3F2(1)
Akihito Ebisu, Katsunori Iwasaki
Using contiguous relations we construct an infinite number of continued fraction expansions for ratios of generalized hypergeometric series 3F2(1). We establish exact error term es…
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…
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…
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…
Special values of the hypergeometric series
Akihito Ebisu
In this paper, we present a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Ap…
Some special values of hypergeometric series related to central values of automorphic -functions
Akihito Ebisu
In a recent work, H.Narita presented problems concerning the strict positivity of central values of certain automorphic -functions in the form of questions regarding special val…
An approximation of a catenoid constructed from piecewise truncated conical minimal surfaces
Akihito Ebisu, Yoshiroh Machigashira
We consider an appoximation of a catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve a…
Apparent singular points of factors of reducible generalized hypergeometric equations
Akihito Ebisu
We consider a reducible generalized hypergeometric equation, whose sub-equation possesses apparent singular points. We determine the polynomial whose roots are these points. We sho…
On a strange evaluation of the hypergeometric series by Gosper
Akihito Ebisu
In a series of letters to D.Stanton, R.W.Gosper presented many strange evaluations of hypergeometric series. Recently, we rediscovered one of the strange hypergeometric identities…