相关论文: The special function "shin", II
The purpose of the work is to furnish a complete study of a discrete and special function, discovered by the author and named with the Arabian letter "SHIN" {The letter SHIN is the thirteenth letter of the Arabian alphabet}. It includes…
This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010…
The results are still valid, however this letter is superceeded by a significantly extended version which is available at astro-ph/0003358 and is scheduled for publication in the ApJ Dec. 10, 2000. We have withdrawn this letter to avoid…
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.
In this paper, we sharpen and generalize Shafer-Fink's double inequality for the arc sine function.
Draft version of an article prepared for the Encyclopedia of Mathematical Physics, Elsevier, to appear in 2006.
This manuscript, a revised version of arXiv:0811.3168v1, was inadvertently submitted as a separate paper. It can now be accessed, including some final corrections for the published version, as arXiv:0811.3168v2.
This text is a commentary on the paper "On some ideals of differentiable functions" of Ren{\'e} Thom which appeared in Volume II of his "Oeuvres Math{\'e}matiques" published by the Soci{\'e}t{\'e} math{\'e}matique de France, s{\'e}rie…
It is suggested that the (p,q)-hypergeometric series studied by Burban and Klimyk (in Integral Transforms and Special Functions, 2 (1994) 15 - 36) can be considered as a special case of a more general (P,Q)-hypergeometric series.
The table of Gradshteyn and Ryzhik contains some integrals that can be expressed in terms of the incomplete beta function. We describe some elementary properties of this function and use them to check some of the formulas in the mentioned…
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
This is the typewritten version of a handwritten manuscript which was completed by Ian G. Macdonald in 1987 or 1988. It is the sequel to the manuscript "Hypergeometric functions I." The two manuscripts are very informal working papers,…
Two typos in the published paper are pointed out. Both are just typos and the calculations in that paper are based on the correct formulism.
Subsequently to the author's preceding paper, we give full proofs of some explicit formulas about factorizations of $K$-$k$-Schur functions associated with any multiple $k$-rectangles.
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…
This is an overview article on the Kontsevich integral written for the Encyclopedia of Mathematical Physics, to be published by Elsevier.
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
We explore some integrals associated with the Riesz function and establish relations to other functions from number theory that have appeared in the literature. We also comment on properties of these functions.
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.