Computing Hypergeometric Solutions of Second Order Linear Differential Equations using Quotients of Formal Solutions and Integral Bases

Imamoğlu, Erdal; Hoeij, Mark van

doi:10.48550/arxiv.1606.01576

Cited by 11 publications

(21 citation statements)

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“…The function G(η) is finally obtained through a rational pull-back of the Gauss hypergeometric function [48], see also [50]. One gets two linearly independent solutions G 1,2 for G(η), related by the transforma-…”

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confidence: 99%

Exact Logarithmic Four-Point Functions in the Critical Two-Dimensional Ising Model

Gori

Viti

2017

Phys. Rev. Lett.

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Based on conformal symmetry we propose an exact formula for the four-point connectivities of Fortuin-Kasteleyn clusters in the critical Ising model when the four points are anchored to the boundary. The explicit solution we found displays logarithmic singularities. We check our prediction using Monte Carlo simulations on a triangular lattice, showing excellent agreement. Our findings could shed further light on the formidable task of the characterization of logarithmic conformal field theories and on their relevance in physics.

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confidence: 99%

Exact Logarithmic Four-Point Functions in the Critical Two-Dimensional Ising Model

Gori

Viti

2017

Phys. Rev. Lett.

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“…In the case of the ρ-parameter a Heun equation [186] remains after separating the first order factorizing terms. Its solution can be given in terms of 2 F 1 -functions with a certain rational argument [185,187] and rational parameters. These structures will later turn out not to occur accidentally.…”

Section: Solutions In the Case Of Non First Order Factorizable Recurr...mentioning

confidence: 99%

Analytic integration methods in quantum field theory: an Introduction

Blümlein¹

2021

Preprint

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“…The homogeneous solutions of Eq. (2.7) can be found in terms of hypergeometric functions at rational argument using the algorithms presented in [17,55]. They read…”

Section: Solutionsmentioning

confidence: 99%

The $ρ$ parameter at three loops and elliptic integrals

Blümlein¹,

Freitas²,

Hoeij³

et al. 2018

Preprint

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We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the ρ parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations do not factorize to first order. The homogeneous solutions to these differential equations are obtained in terms of hypergeometric functions at rational argument. These hypergeometric functions can further be mapped to complete elliptic integrals, and the inhomogeneous solutions are expressed in terms of a new class of integrals of combined iterative non-iterative nature.

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Computing Hypergeometric Solutions of Second Order Linear Differential Equations using Quotients of Formal Solutions and Integral Bases

Cited by 11 publications

References 0 publications

Exact Logarithmic Four-Point Functions in the Critical Two-Dimensional Ising Model

Exact Logarithmic Four-Point Functions in the Critical Two-Dimensional Ising Model

Analytic integration methods in quantum field theory: an Introduction

The $ρ$ parameter at three loops and elliptic integrals

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