Gamma series associated to elements satisfying regularized double shuffle relations
Let \(K\) be a field of characteristic zero, \(R\) a commutative \(K\)-algebra, \( \Phi(x_0,x_1)\in R\langle\langle x_0,x_1\rangle\rangle\) with regularized double shuffle relations. The author defines a gamma series \(\Gamma_\Phi(s)\in 1+s^2Rs\) and proves that the associated beta series is the image of \(\Phi_Y(x_0,x_1)\) in the commutative formal power series ring \(Rx_0,x_1\), where \(\Phi_Y(x_0,x_1)=1+\Phi_1 x_1\), \(\Phi=1+\Phi_0x_0+\Phi_1x_1\).
scientific article; zbMATH DE number 5654992
scientific article