Coxeter group actions on Saalschützian \(_4F_3(1)\) series and very-well-poised \(_7F_6(1)\) series (Q641670)

The author considers a function \(L(\bar{x})= L(a,b,c,d;e;f, g)\) which can be written as a linear combination of two Saalschützian \(_4F_3(1)\) hypergeometric series or as very well-poised \(_7F_6(1)\) hypergeometric series. The author explores two-term and three-term relations satisfied by the L-function and shows that this relation implies that the Coxeter group \(W(D_5)\) containing 1920 elements is an invariance group for \(L(\bar{x})\) .