scholarly journals Tensor integrand reduction via Laurent expansion

2016 ◽  
Vol 2016 (6) ◽  
Author(s):  
Valentin Hirschi ◽  
Tiziano Peraro
Keyword(s):  
Laurent Expansion

scholarly journals Laurent expansion of harmonic zeta functions

2020 ◽  
Vol 491 (1) ◽  
pp. 124309
Author(s):  
Bernard Candelpergher ◽  
Marc-Antoine Coppo
Keyword(s):  
Zeta Functions ◽  
Laurent Expansion

Laurent expansion of Dirichlet series-II

1987 ◽  
Vol 103 (1) ◽  
pp. 1-5 ◽  
Author(s):  
U. Balakrishnan
Keyword(s):  
Dirichlet Series ◽  
Laurent Expansion

scholarly journals THE SCALAR BOX INTEGRAL AND THE MELLIN–BARNES REPRESENTATION

2011 ◽  
Vol 26 (15) ◽  
pp. 2557-2568 ◽  
Author(s):  
P. VALTANCOLI
Keyword(s):  
Analytic Continuation ◽  
Hypergeometric Functions ◽  
Laurent Expansion

We solve exactly the scalar box integral using the Mellin–Barnes representation. First we recognize the hypergeometric functions resumming the series coming from the scalar integrals, then we perform an analytic continuation before applying the Laurent expansion in ϵ = (d-4)/2 of the result.

scholarly journals Laurent expansion of the inverse of perturbed, singular matrices

2015 ◽  
Vol 299 ◽  
pp. 307-319 ◽  
Author(s):  
Pedro Gonzalez-Rodriguez ◽  
Miguel Moscoso ◽  
Manuel Kindelan
Keyword(s):  
Laurent Expansion ◽  
Singular Matrices

scholarly journals The a-points of Faber polynomials for a special function

1970 ◽  
Vol 11 (1) ◽  
pp. 1-6
Author(s):  
Hassoon S. Al-Amiri
Keyword(s):  
Analytic Function ◽  
Power Series ◽  
Analytic Continuation ◽  
Special Function ◽  
Laurent Expansion ◽  
Faber Polynomials ◽  
Analytic Element ◽  
Formal Expansion ◽  
Image Position

Let f(ζ) be a power series of the formwhere lim sup |an|1/n < ∞. The Faber polynomials {fn(ζ)} (n = 0, 1, 2, …) are the polynomial parts of the formal expansion of (f(ζ))n about ζ = ∞. Series (1) defines an analytic element of an analytic function which we designate as w = f(ζ). Since at ζ = ∞ the analytic element is univalent in some neighborhood of infinity; thus the inverse of this element is uniquely determined in some neighborhood of w= ∞, and has a Laurent expansion of the formwhere lim sup |bn|1/n = p < ∞. Let ζ = g(w) be this single-valued function defined by (2) in |w| > p. No analytic continuation of g(w) will be considered.

scholarly journals On certain sums over ordinates of zeta-zeros II

2019 ◽  
Author(s):  
Andriy Bondarenko ◽  
Aleksandar Ivić ◽  
Eero Saksman ◽  
Kristian Seip
Keyword(s):  
Analytic Continuation ◽  
Critical Line ◽  
Laurent Expansion ◽  
Second Moment ◽  
International Audience ◽  
Complex Zeros ◽  
Gamma S

International audience Let γ denote the imaginary parts of complex zeros ρ = β + iγ of ζ(s). The problem of analytic continuation of the function $G(s) :=\sum_{\gamma >0} {\gamma}^{-s}$ to the left of the line $\Re{s} = −1 $ is investigated, and its Laurent expansion at the pole s = 1 is obtained. Estimates for the second moment on the critical line $\int_{1}^{T} {| G (\frac{1}{2} + it) |}^2 dt $ are revisited. This paper is a continuation of work begun by the second author in [Iv01].

scholarly journals The Hilbert series of SL2-invariants

2019 ◽  
Vol 22 (07) ◽  
pp. 1950017
Author(s):  
Pedro de Carvalho Cayres Pinto ◽  
Hans-Christian Herbig ◽  
Daniel Herden ◽  
Christopher Seaton
Keyword(s):  
Hilbert Series ◽  
Laurent Expansion ◽  
Dimensional Representation ◽  
Invariant Polynomials ◽  
Finite Dimensional Representation ◽  
Finite Dimensional ◽  
Complex Coefficients

Let [Formula: see text] be a finite-dimensional representation of the group [Formula: see text] of [Formula: see text] matrices with complex coefficients and determinant one. Let [Formula: see text] be the algebra of [Formula: see text]-invariant polynomials on [Formula: see text]. We present a calculation of the Hilbert series [Formula: see text] as well as formulas for the first four coefficients of the Laurent expansion of [Formula: see text] at [Formula: see text].

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