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Elliptic hypergeometric integrals Eric M. Rains Department of Mathematics California Institute of Technology MPIM Oberseminar, Bonn, 24/7/2008 Hypergeometric integrals Gaussian…

Some problems on hypergeometric integrals associated with hypersphere arrangements in memory of Tetsusuke Ohkawa Kazuhiko Aomoto and Yoshinori Machida 2015 Aug 28-30 1 Introduction…

ar X iv :1 30 9 45 68 v1 m at h C A 1 8 Se p 20 13 HYPERGEOMETRIC FUNCTIONS I IAN G MACDONALD Contents Foreword 1 1 2 2 Particular cases 4 3 Integral formulae 7 4 Gauss Saalschutz…

Multiplication and Translation Formulas for the Generalized Hypergeometric Functions and Their Applications Zhongfeng Sun and Huizeng Qin Abstract—In his paper, the following…

Feynman integrals and algebraic geometry Matilde Marcolli 2009 Based on: joint work with P. Aluffi, arXiv:0807.1690, arXiv:0811.2514, arXiv:0901.2107. Quantum Fields and…

HYPERGEOMETRIC FUNCTIONS I IAN G MACDONALD Contents Foreword 1 1 2 2 Particular cases 4 3 Integral formulae 7 4 Gauss Saalschutz summation 12 5 Integral formulae II 15 6…

Contents Foreword 1 1. 2 2. Particular cases 4 3. Integral formulae 7 4. Gauss & Saalschutz summation 12 5. Integral formulae II 15 6. Hypergeometric functions with parameter

Evaluation of integrals Lecture 18 Evaluation of integrals Evaluation of certain contour integrals: Type I Type I: Integrals of the form∫ 2π 0 F cos θ sin θ dθ If we…

MULTIPLE INTEGRALS 15 POLAR COORDINATES In plane geometry, the polar coordinate system is used to give a convenient description of certain curves and regions. See Section…

Beta Integrals Euler Beta Integral Selberg Integral An Selberg Integral Beta Integrals S. Ole Warnaar Department of Mathematics and Statistics Beta Integrals Euler Beta Integral…

Lindelöf integral representations and asymptotic analysis of a certain power series with closed-form coefficients Stefan Gerhold joint work with P Flajolet and B Salvy…

Double Integrals Introduction * Volume and Double Integral z=f(x,y) ≥ 0 on rectangle R=[a,b]×[c,d] S={(x,y,z) in R3 | 0 ≤ z ≤ f(x,y), (x,y) in R} Volume of S = ? *…

Line, Surface and Volume Integrals 1 Line integrals ∫ C φdr, ∫ C a · dr, ∫ C a× dr (1) (φ is a scalar field and a is a vector field) We divide the path C joining…

Slide 1 Chapter 15 – Multiple Integrals 15.4 Double Integrals in Polar Coordinates 15.4 Double Integrals in Polar Coordinates 1 Objectives: Determine how to express double…

Chapter 2 Fourier Integrals 2.1 L1-Theory Repetition: R = (−∞,∞), f ∈ L1(R) ⇔ ∫ ∞ −∞ |f(t)|dt < ∞ (and f measurable) f ∈ L2(R) ⇔ ∫ ∞ −∞…

WELL-POISED HYPERGEOMETRIC SERVICE FOR DIOPHANTINE PROBLEMS OF ZETA VALUES WADIM ZUDILIN Abstract It is explained how the classical concept of well-poised hyperge- ometric…

Lecture 4: Multiple Integrals • Recall physical interpretation of a 1D integral as area under curve • Divide domain a,b into n strips, each of width δrk , k=1,2...,n…

Fourier Integrals Fourier Transforms FOURIER TRANSFORMS G Ramesh 28th Sep 2015 Fourier Integrals Fourier Transforms OUTLINE 1 FOURIER INTEGRALS 2 FOURIER TRANSFORMS Fourier…

1. Section 5.3 Evaluating Definite Integrals Math 1a Introduction to Calculus April 16, 2008 Announcements ◮ Midterm is finished: ¯ ≈ 43, σ ≈ 6. x ◮ Midterm III…

StewartCalcET8_15_01.ppt [Read-Only]15.1 Double Integrals over Rectangles 2 Review of the Definite Integral First let’s recall the basic facts concerning definite integrals