2 edition of **Arrangements and hypergeometric integrals** found in the catalog.

Arrangements and hypergeometric integrals

Peter Orlik

- 51 Want to read
- 30 Currently reading

Published
**2001**
by Mathematical Society of Japan in Tokyo
.

Written in English

- Hypergeometric functions.,
- Combinatorial geometry.,
- Combinatorial enumeration problems.,
- Lattice theory.

**Edition Notes**

Includes bibliographical references.

Statement | Peter Orlik, Hiroaki Terao. |

Series | MSJ memoirs -- v. 9 |

Contributions | Terao, Hiroaki, 1951- |

Classifications | |
---|---|

LC Classifications | QA353.H9 O75 2001 |

The Physical Object | |

Pagination | ix, 112 p. : |

Number of Pages | 112 |

ID Numbers | |

Open Library | OL20987708M |

ISBN 10 | 4931469108 |

Hyperplane arrangement Geometric semilattice Orlik–Solomon algebra Divisor Singularity Complement Homotopy type Poincaré polynomial Ball quotient Logarithmic form Hypergeometric integral This is a preview of subscription content, log in to check access. Hypergeometric Functions and Arrangements of Hyperplanes Michel Jambu Professor Emeritus Laboratoire J.A. Dieudonn´e, UMR CNRS John Wallis in his book Arithmetica Inﬁnitorum. Hypergeometric series were studied by The beta function is the integral of a product of powers of linear functions over a segment.

ADVANCES IN MATHEMAT () Generalized Euler Integrals and A-Hypergeometric Functions 1. M. GELFAND,* M. M. KAPRANOV,t AND A. V. ZELEVINSKYt * A. N. Belozersky Laboratory of Molecular Biology and Bioorganic Chemistry, Laboratory Building A, Moscow State University, Moscow , USSR t Department of Mathematics, Cornell University, Ithaca, NY . This book is organized as follows. Part I contains a very short but detailed exposition of the essential material of string theory required for a grounded understanding of the supersymmetric matrix models presented in part II. Part II is the core of this book. The beta integral method and hypergeometric transformations.

Ann. Inst. Fourier, Greno 1 () STOKES MATRICES OF HYPERGEOMETRIC INTEGRALS by Alexey GLUTSYUK & Christophe SABOT Abstract. — . The confluent hypergeometric function, denoted by 1F1(a; c; z), is defined by() 1F1(a; c; z) =(a)nz n(c)nn!with (a)n being the rising factorial(a)n:.

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In mathematics, the Gaussian or ordinary hypergeometric function 2 F 1 (a,b;c;z) is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting is a solution of a second-order linear ordinary differential equation (ODE).

Every second-order linear ODE with three regular singular points can be transformed into this. This is an outline of the Aomoto–Gelfand theory of multivariable hypergeometric integrals and Varchenko's formula for the determinant of the period matrix of the hypergeometric pairing.

A significant feature of this work is the use of the theory of arrangements of hyperplanes to transform a problem in analysis into one in by: 2.

Orlik and H. Terao are leading specialists in the theory of arrangements and the co-authors of the well-known book "Arrangements of Hyperplanes." In this monograph, they give an introductory survey which also contains the recent progress in the theory of hypergeometric functions.

Arrangements and hypergeometric integrals. Tokyo: Mathematical Society of Japan, (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Peter Orlik; Hiroaki Terao.

The n-dimensional hypergeometric integrals associated with a hypersphere arrangement are formulated by the pairing of n-dimensional twisted cohomology and its dual. Book On Congruence Monodromy Problems () Ihara, Yasutaka.

Book. Multivariate Statistics () Eaton, Morris L. Book. Complex Datasets and Inverse Problems () Arrangements and Hypergeometric Integrals () Orlik, Peter and Terao, Hiroaki. Book Dynamics & Stochastics () Denteneer, Dee, Hollander. Integral Representation Hypergeometric Function Integral Solution Hypergeometric Series Partial Fraction Expansion These keywords were added by machine and not by the authors.

This process is experimental and the keywords may be updated as the learning algorithm improves. Author: S.B.

Yakubovich,Yury Luchko; Publisher: Springer Science & Business Media ISBN: Category: Mathematics Page: View: DOWNLOAD NOW» The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational.

direct link between the gamma and hypergeometric functions, and most hypergeometric identities can be more elegantly expressed in terms of the gamma function. In the words of Andrews et al., “the gamma function and beta integrals are essential to understanding hypergeometric functions” (cf.

Two more hypergeometric integral equations - Volume 63 Issue 4 - E. Love Due to unplanned maintenance of the back-end systems supporting article purchase on Cambridge Core, we have taken the decision to temporarily suspend article purchase for the foreseeable future.

This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system.

We construct imaginary cycles for hypergeometric integrals associ- ated with a hypersphere arrangement and discuss the relation between the twisted rational de.

AbstractWe provide an explicit analytical representation for a number of logarithmic integrals in terms of the Lerch transcendent function and other special functions. The integrals in question will be associated with both alternating harmonic numbers and harmonic numbers with positive terms.

A few examples of integrals will be given an identity in terms of some special functions including the. Arrangements and hypergeometric integrals An affine arrangement of hyperplanes is a finite collection of one-codimensional affine linear spaces in C n.

Orlik and H. Terao are leading specialists in the theory of arrangements and the co-authors of the well-known book ``Arrangements. The classical story - of the hypergeometric functions, the configuration space of 4 points on the projective line, elliptic curves, elliptic modular functions and the theta functions - now evolves, in this book, to the story of hypergeometric funktions in 4 variables, the configuration space of 6 points in the projective plane, K3 surfaces, theta functions in 4 s: 2.

DESY 16{ DO{TH 16/14 May Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams J. Ablingera, J. Bl umlein b, A. De Freitasb, M. van Hoeijc, E. Imamogluc, C.G. Raabd, C.-S. Radua, and C. Schneidera aResearch Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraˇe 69, A Linz, Austria.

One of the rst issues about special functions is the set of four books, published between and J. Tannery, N. Molk, El ements de la th eorie des fonctions elliptiques I, II: Calcul di erentiel I.

has mild singularities; as functions deﬁned by integrals such as the Mellin-Barnes integral. For one-variable hypergeometric functions this interplay has been well understood for several decades. In the several variables case, on the other hand, it is possible to extend each one of these approaches but one may get slightly diﬀerent results.

cal Gauss hypergeometric function 2F 1, Gauss conﬂuent hypergeometric function ϕ(α,β) p (b;c;z) function and generalized hypergeometric function pFq.

A specimen of some of these interesting applications of our main integral formulas are pre-sented brieﬂy. Mathematics Subject Classiﬁcation: 33B20, 33C05, 33C20, 33C engineering Applications.

On specializing the parameters, we can easily obtain some new integrals by rathie and others which are given in Book of Mathai and Saxena. Key Words: Generalized Hypergeometeric functions, Gamma function and integrals. INTRODUCTION The definition of the Gauss’s Hypergeometric Series [6] and €which can a,b.

The Barnes Integral for the Hypergeometric Function Contiguous Relations Dilogarithms Binomial Sums Dougall's Bilateral Sum Fractional Integration by Parts and Hypergeometric Integrals 3 Hypergeometric Transformations and Identities Quadratic Transformations The Arithmetic-Geometric Mean and Elliptic Integrals.integrals of generic graphs as linear combinations of their canonical series.

We evaluate several Feynman integrals with arbitrary non-integer powers in the propagators using the canonical series algorithm. Contents 1. Introduction 2 2. A-hypergeometric functions and their representations 3 Integrals like that of Selberg arise as integral representations of these generalized hypergeometric functions over hyperplane arrangements.

In the fourth and final chapter the authors prove a classical theorem of G. D. Birkhoff on the asymptotic behavior of solutions of difference equations, and apply it to the foregoing theory.