arXiv subjects

Yasushi Kajihara

Publications and source records attributed to Yasushi Kajihara.

5 recordsLinked to original sources

arXiv2014

Symmetry Groups of $A_n$ Hypergeometric Series

Structures of symmetries of transformations for Holman-Biedenharn-Louck $A_n$ hypergeometric series: $A_n$ terminating balanced ${}_4 F_3$ series and $A_n$ elliptic ${}_{10} E_9$ series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of $A_n$ hypergeometric series are given. Among them, a "periodic" affine Coxeter group which seems to be new in the literature arises as an invariance group for a class of $A_n$ ${}_4 F_3$ series.

math.CA↗

arXiv2014

Multiple basic hypergeometric transformation formulas arising from the balanced duality transformation

Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking certain limits of the balanced duality transformation. By combining some of them, some transformation formulas for $A_n$ basic hypergeometric series is given. They include some generalizations of Watson, Sears and ${}_8 W_7$ transformations.

math.CA↗

arXiv2014

Transformation formulas for bilinear sums of basic hypergeometric series

A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic hypergeometric series of type $A$ with different dimensions and it can be considered as a generalization of Whipple-Sears transformation formula for terminating balanced ${}_4 ϕ_3$ series. As an application of the master formula, one variable cases of some transformation formulas for bilinear sums of basic hypergeometric series are given as examples. The bilinear transformation formulas seem to be new in the literature even in one variable case.

math.CA↗

arXiv2003

Multiple elliptic hypergeometric series --An approach from the Cauchy determinant--

A multiple generalization of elliptic hypergeometric series is investigated and a duality transformation for multiple hypergeometric series is proposed. Our duality transformation obtained from an identity arising from the Cauchy determinant formula for Weierstrass sigma functions, by spcialization of a particular form.

math.CA↗

arXiv1998

Raising operators of row type for Macdonald polynomials

Raising operators of row type are constructed by means of an interpolation method. These are a dual version of the raising operators of column type by A.N.Kirillov and M.Noumi. An extension of the q-binomial coefficients is introduced in relation to the raising operators.

math.QA↗