Related papers: Errata, updates of the references, etc., for the b…
After reviewing some fundamental facts from the theory of theta hypergeometric series we derive, using indefinite summation, several summation, transformation, and expansion formulas for multibasic theta hypergeometric series. Some of the…
We give an overview of some of the main results from the theories of hypergeometric and basic hypergeometric series and integrals associated with root systems. In particular, we list a number of summations, transformations and explicit…
This is a list of corrections for the book: J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\ Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors hope that this…
We present some elementary derivations of summation and transformation formulas for q-series, which are different from, and in several cases simpler or shorter than, those presented in the Gasper and Bahman [1990] "Basic Hypergeometric…
This survey article (which will appear as a chapter in the book ``Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions'', Springer-Verlag) provides a small collection of basic material on multiple…
Errata are given for "The Higgs Hunter's Guide". These errata should be applied to the second printing of the book, dated 1991. The second printing has already corrected numerous errors and misprints contained in the originally published…
Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.
We derive two generalizations of Gasper's transformation formula for basic hypergeometric series. Using these generalized formulas, we give explicit expressions for the coefficients of three-term relations for the basic hypergeometric…
Several new $q$-supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the…
A mistake is pointed out in EGA I, Elements of algebraic geometry, concerning corollary (2.4.4) which is not correct. Quite likely, the hitch has already been noticed, and reported, but we know not who, nor where. New research is…
This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.
We examine the convergence of $q$-hypergeometric series when $|q|=1$.
In this paper, we establish three new and general transformations with sixteen parameters and bases via Abel's lemma on summation by parts. As applications, we set up a lot of new transformations of basic hypergeometric series. Among…
An elementary proof is given for a nonterminating "strange" cubic $_7F_6$-series summation formula of Gasper and Rahman, through the modified Abel lemma on summation by parts. As a byproduct, an interesting nonterminating…
This is a survey article, based on the author's lectures in the 2015 Current developments in Mathematics meeting; published in "Current developments in Mathematics". Version 2, references corrected and added.
This note covers two parts. The first one provides an errata to the paper "Numerical and analytical modeling of busbar systems". We mainly give the correction for three equations affected by a typographical mistake. Despite the corrections…
This article serves as errata of the book "Energy of knots and conformal geometry", Series on Knots and Everything Vol. 33, World Scientific, Singapore, 304 pages, (2003). (ver. 27/05/2007)
Employing a quadratic transformation formula of Rahman and the method of `creative microscoping' (introduced by the author and Zudilin in 2019), we provide some new $q$-supercongruences for truncated basic hypergeometric series. In…
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 hypergeometric identity, which includes some of these identities as…
In 2017, He [Proc. Amer. Math. Soc. 145 (2017), 501--508] established two spuercongruences on truncated hypergeometric series and further proposed two related conjectures. Subsequently, Liu [Results Math. 72 (2017), 2057--2066] extended…