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- W3100996920 abstract "We prove Laporta’s conjecture which relates the 4-loop sunrise diagram in 2-dimensional quantum field theory to Watson’s integral for 4-dimensional hypercubic lattice. We also establish several related integral identities proposed by Laporta, including a reduction of the 4-loop sunrise diagram to special values of Euler’s gamma function and generalized hypergeometric series: $$begin{aligned}&frac{4 pi ^{5/2}}{sqrt{3}}left{ frac{sqrt{3} }{2^6 }left[ frac{Gamma left( frac{1}{3}right) }{sqrt{pi }}right] ^9, _4F_3left( left. begin{array}{c}frac{1}{6},frac{1}{3},frac{1}{3},frac{1}{2} frac{2}{3},frac{5}{6},frac{5}{6}end{array} right| 1right) -frac{2^{4}}{3}left[ frac{sqrt{pi }}{Gamma left( frac{1}{3}right) }right] ^9, _4F_3left( left. begin{array}{c}frac{1}{2},frac{2}{3},frac{2}{3},frac{5}{6} frac{7}{6},frac{7}{6},frac{4}{3}end{array} right| 1right) right} . end{aligned}$$" @default.
- W3100996920 created "2020-11-23" @default.
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- W3100996920 date "2019-01-29" @default.
- W3100996920 modified "2023-09-26" @default.
- W3100996920 title "On Laporta’s 4-loop sunrise formulae" @default.
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- W3100996920 doi "https://doi.org/10.1007/s11139-018-0090-z" @default.
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