scholarly journals The Multivariable Aleph-function involving the Generalized Mellin-Barnes Contour Integrals

Cubo (Temuco) ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 351-359
Author(s):  
Abdi Oli ◽  
Kelelaw Tilahun ◽  
G. V. Reddy
Keyword(s):  
Contour Integrals

scholarly journals Asymptotic symmetries and celestial CFT

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Laura Donnay ◽  
Sabrina Pasterski ◽  
Andrea Puhm
Keyword(s):  
Principal Series ◽  
Finite Energy ◽  
Continuous Series ◽  
Asymptotic Symmetry ◽  
Null Infinity ◽  
Conformal Dimension ◽  
Contour Integrals ◽  
Celestial Sphere ◽  
Goldstone Modes ◽  
Asymptotic Symmetries

Abstract We provide a unified treatment of conformally soft Goldstone modes which arise when spin-one or spin-two conformal primary wavefunctions become pure gauge for certain integer values of the conformal dimension ∆. This effort lands us at the crossroads of two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. Finite energy wavefunctions are captured by the principal continuous series ∆ ∈ 1 + iℝ and form a complete basis. We show that conformal primaries with analytically continued conformal dimension can be understood as certain contour integrals on the principal series. This clarifies how conformally soft Goldstone modes fit in but do not augment this basis. Conformally soft gravitons of dimension two and zero which are related by a shadow transform are shown to generate superrotations and non-meromorphic diffeomorphisms of the celestial sphere which we refer to as shadow superrotations. This dovetails the Virasoro and Diff(S2) asymptotic symmetry proposals and puts on equal footing the discussion of their associated soft charges, which correspond to the stress tensor and its shadow in the two-dimensional celestial CFT.

A Simplification in Certain Contour Integrals

1977 ◽  
Vol 84 (6) ◽  
pp. 467 ◽  
Author(s):  
Harold P. Boas ◽  
Eduardo Friedman
Keyword(s):  
Contour Integrals

Contour Integrals

2009 ◽  
pp. 259-303
Author(s):  
Hiroyuki Shima ◽  
Tsuneyoshi Nakayama
Keyword(s):  
Contour Integrals

Contour integrals of analytic functions given on a grid in the complex plane

2020 ◽  
Author(s):  
Bengt Fornberg
Keyword(s):  
Complex Plane ◽  
Line Segment ◽  
Analytic Functions ◽  
Trapezoidal Rule ◽  
Contour Integrals ◽  
Grid Points ◽  
Maclaurin Formula

Abstract Ability to evaluate contour integrals is central to both the theory and the utilization of analytic functions. We present here a complex plane realization of the Euler–Maclaurin formula that includes weights also at some grid points adjacent to each end of a line segment (made up of equispaced grid points, along which we use the trapezoidal rule). For example, with a $5\times 5$ ‘correction stencil’ (with weights about two orders of magnitude smaller than those of the trapezoidal rule), the accuracy is increased from $2$nd to $26$th order.

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