Is it possible to write simple expressions for the Gauss hypergeometric functions F(1,15/8,23/8;z)
and F(1,1/8,9/8,z)
Exactly how simple is simple? Simplicity is in the eye of the beholder!
For systematic lists of some of the many thousands of published identities involving the hypergeometric function, see the reference works by Arthur Erdélyi, Wilhelm Magnus, and Fritz Oberhettinger et al. (1953), Abramowitz & Stegun (1965), and Daalhuis (2010).(from Wiki)