Let K be a field of characteristic 0, and R be a commutative K -algebra. Let Φ ( x 0 , x 1 ) be an element in R 《 x 0 , x 1 》 with regularized double shuffle relations. We define a gamma series Γ Φ ( s ) ∈ 1 + s 2 R 〚 s 〛 associated to Φ. We prove that the associated beta series is just the image of Φ Y ( x 0 , x 1 ) in the commutative formal power series ring R 〚 x 0 , x 1 〛 , where if Φ = 1 + Φ 0 x 0 + Φ 1 x 1 , then Φ Y = 1 + Φ 1 x 1 . We also give some equivalent conditions for the reflection formula of the gamma series Γ Φ ( s ) .